From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 48/CH2/EX2.1/eg_2_1.sce   | 22 ++++++++++++
 48/CH2/EX2.11/eg_2_11.sce | 23 +++++++++++++
 48/CH2/EX2.12/eg_2_12.sce | 34 +++++++++++++++++++
 48/CH2/EX2.15/eg_2_15.sce | 31 +++++++++++++++++
 48/CH2/EX2.16/eg_2_16.sce | 12 +++++++
 48/CH2/EX2.2/eg_2_2.sce   | 85 +++++++++++++++++++++++++++++++++++++++++++++++
 48/CH2/EX2.4/eg_2_4.sce   | 25 ++++++++++++++
 48/CH2/EX2.5/eg_2_5.sce   | 61 ++++++++++++++++++++++++++++++++++
 48/CH2/EX2.6/eg_2_6.sce   | 34 +++++++++++++++++++
 48/CH2/EX2.7/eg_2_7.sce   | 31 +++++++++++++++++
 10 files changed, 358 insertions(+)
 create mode 100755 48/CH2/EX2.1/eg_2_1.sce
 create mode 100755 48/CH2/EX2.11/eg_2_11.sce
 create mode 100755 48/CH2/EX2.12/eg_2_12.sce
 create mode 100755 48/CH2/EX2.15/eg_2_15.sce
 create mode 100755 48/CH2/EX2.16/eg_2_16.sce
 create mode 100755 48/CH2/EX2.2/eg_2_2.sce
 create mode 100755 48/CH2/EX2.4/eg_2_4.sce
 create mode 100755 48/CH2/EX2.5/eg_2_5.sce
 create mode 100755 48/CH2/EX2.6/eg_2_6.sce
 create mode 100755 48/CH2/EX2.7/eg_2_7.sce

(limited to '48/CH2')

diff --git a/48/CH2/EX2.1/eg_2_1.sce b/48/CH2/EX2.1/eg_2_1.sce
new file mode 100755
index 000000000..21e773b09
--- /dev/null
+++ b/48/CH2/EX2.1/eg_2_1.sce
@@ -0,0 +1,22 @@
+clear;
+clc;
+//lower=input("input the lower limit of the set");
+//upper=input("input the upper limit of the set");
+lower=1;    //lower limit of the set 
+upper=10;   //upper limit of the set
+temp=lower;
+h=1;i=1;
+while(temp<=upper)
+    if(modulo(temp,2)==0)       //checking whether a number is even or not
+        e(h)=temp;
+        h=h+1;
+    else
+        o(i)=temp;             //odd number 
+        i=i+1;
+    end
+    temp=temp+1;
+end;
+disp("the set of even number between the limits")
+disp(e);
+disp("the set of odd number between the limits")
+disp(o);
diff --git a/48/CH2/EX2.11/eg_2_11.sce b/48/CH2/EX2.11/eg_2_11.sce
new file mode 100755
index 000000000..520598f91
--- /dev/null
+++ b/48/CH2/EX2.11/eg_2_11.sce
@@ -0,0 +1,23 @@
+clear;
+clc;
+//N=input("enter the number for which divisibilty ");
+N=45;        //divident
+h=1;
+for i=1:N        //finding all the divisors of 45
+    if(modulo(N,i)==0)
+        r(h)=i;
+        h=h+1;
+     end
+end
+n=max(size(r));
+disp("Hasse Diagram")       //displaying in the form of hasse diagram
+disp("------------")
+disp(r(n));
+h=2;
+for i=n-1:-2:3
+    disp("-----------");
+    disp(r(i),r(i-1));
+    h=h+1;
+end
+disp("----------")
+disp(r(1));
diff --git a/48/CH2/EX2.12/eg_2_12.sce b/48/CH2/EX2.12/eg_2_12.sce
new file mode 100755
index 000000000..2378410ee
--- /dev/null
+++ b/48/CH2/EX2.12/eg_2_12.sce
@@ -0,0 +1,34 @@
+clear
+clc
+N=4;
+//defining all the partial ordered sets
+s(1,:)=[1 0];
+s(2,:)=[0 1];
+s(3,:)=[0 0];
+s(4,:)=[1 1];
+//Finding 
+a=1;b=1;
+for i=1:1:N            //sorting based on the level
+    for j=i:1:N
+        if(i~=j)
+            u=s(i,1)+s(i,2);
+            v=s(j,1)+s(j,2);
+            if(u<v)
+                temp(1)=s(i,1);
+                temp(2)=s(i,2);
+                s(i,1)=s(j,1);
+                s(i,2)=s(j,2);
+                s(j,1)=temp(1);
+                s(j,2)=temp(2);
+            end
+        end
+    end
+end
+// displaying in the form of hasse graph form
+disp("1st stage of Hasse diagram");
+disp(s(1,:));
+disp("2nd stage of Hasse diagram");
+disp(s(2,:));
+disp(s(3,:));
+disp("3rd stage of Hasse diagram");
+disp(s(4,:));
\ No newline at end of file
diff --git a/48/CH2/EX2.15/eg_2_15.sce b/48/CH2/EX2.15/eg_2_15.sce
new file mode 100755
index 000000000..c7a250e6c
--- /dev/null
+++ b/48/CH2/EX2.15/eg_2_15.sce
@@ -0,0 +1,31 @@
+clear
+clc
+N=3;
+s=['a' 'b' 'c'];        //set for which lattice should be defined
+for i=2:2^3
+    s(i,:)=s(1,:);
+end
+//defining 2nd level vertices of the lattice
+for i=2:4
+    s(i,i-1)='0';
+end
+//defining 3rd level vertices of the lattice
+for i=5:6
+    s(i,i-4)='0';
+    s(i,i-3)='0';
+end
+s(7,1)='0';s(7,3)='0';
+//defining the final level of vertices of the lattice
+s(8,:)=['0' '0' '0'];
+disp("1st level");
+disp(s(1,:));
+disp("2nd level");
+disp(s(2,:));
+disp(s(3,:));
+disp(s(4,:));
+disp("3rd level");
+disp(s(5,:));
+disp(s(6,:));
+disp(s(7,:));
+disp("4th level");
+disp(s(8,:));
\ No newline at end of file
diff --git a/48/CH2/EX2.16/eg_2_16.sce b/48/CH2/EX2.16/eg_2_16.sce
new file mode 100755
index 000000000..dd4507ba8
--- /dev/null
+++ b/48/CH2/EX2.16/eg_2_16.sce
@@ -0,0 +1,12 @@
+clear;
+clc;
+par1=['ab','cde','fh','gi'];    //initial partitions par1
+par2=['abc','de','fg','hi'];    //partition 2 
+//par=par1+par2;
+//lub-lower upper bound
+par_lub=['abcde','fghi'];
+disp(par_lub);
+//par=par1.par2
+//glb-greatest lower bound
+par_glb=['ab','c','de','f','g','h','i'];
+disp(par_glb);
\ No newline at end of file
diff --git a/48/CH2/EX2.2/eg_2_2.sce b/48/CH2/EX2.2/eg_2_2.sce
new file mode 100755
index 000000000..a8d16dadc
--- /dev/null
+++ b/48/CH2/EX2.2/eg_2_2.sce
@@ -0,0 +1,85 @@
+clear;
+clc;
+//N=input("enter the elements in the set");
+//n=1;
+//while(n<=N)
+//    i(n)=input("enter the elements of first set");
+//    n=n+1;
+//end;
+N=6;
+i(1)='f1';i(2)='f2';i(3)='f3';i(4)='f4';i(5)='f5';i(6)='f6';
+disp("null set");   //since null set is subset of any set.
+for a=1:1:N        //set of single elements
+    disp(i(a));
+end
+c=1;
+for a=1:1:N-1            //set of two elements
+    for b=a:1:N
+        if(a~=b)
+          m(c,1)=i(a);
+          m(c,2)=i(b);
+          c=c+1;
+        end
+    end;
+end;
+disp(m);
+d=1;
+for a=1:1:N            //set of three elements
+    for b=a:1:N
+        for c=b:1:N
+            if((a~=b)&(b~=c)&(c~=a))
+               p(d,1)=i(a);
+               p(d,2)=i(b);
+               p(d,3)=i(c);
+               d=d+1;
+            end
+        end
+    end
+end
+disp(p);
+e=1;
+for a=1:1:N            //set of four elements
+    for b=a:1:N
+        for c=b:1:N
+            for d=c:1:N
+                if((a~=b)&(b~=c)&(c~=d)&(d~=a)&(b~=d)&(a~=c))
+                   q(e,1)=i(a);
+                   q(e,2)=i(b);
+                   q(e,3)=i(c);
+                   q(e,4)=i(d)
+                   e=e+1;
+                end
+            end
+        end
+    end
+end
+disp(q);
+f=1;
+for a=1:1:N            //set of five elements
+    for b=a:1:N
+        for c=b:1:N
+            for d=c:1:N
+                for e=d:1:N
+                    if((a~=b)&(b~=c)&(c~=d)&(d~=e)&(e~=a)&(a~=c)&(a~=d)&(b~=d)&(c~=e)&(b~=e))
+                       r(f,1)=i(a);
+                       r(f,2)=i(b);
+                       r(f,3)=i(c);
+                       r(f,4)=i(d);
+                       r(f,5)=i(e);
+                       f=f+1;
+                    end
+                end
+            end
+        end
+    end
+end
+disp(r);
+for a=1:1:N            //set of six elements
+    s(1,1)=i(1);
+    s(1,2)=i(2);
+    s(1,3)=i(3);
+    s(1,4)=i(4);
+    s(1,5)=i(5);
+    s(1,6)=i(6);
+end
+disp(s);
\ No newline at end of file
diff --git a/48/CH2/EX2.4/eg_2_4.sce b/48/CH2/EX2.4/eg_2_4.sce
new file mode 100755
index 000000000..131e07aaf
--- /dev/null
+++ b/48/CH2/EX2.4/eg_2_4.sce
@@ -0,0 +1,25 @@
+clear;
+clc;
+N1=2;
+N2=3;
+//n=1;
+//while(n<=N1)
+//    i(n)=input("enter the elements of first set");
+//    n=n+1;
+//end;
+i=['p' 'q'];    //set A
+//n=1;
+//while(n<=N2)
+//    j(n)=input("enter the elements of second set");
+//    n=n+1;
+//end;
+j=['r' 's' 't'];    //set B
+c=1;d=1;
+for a=1:1:N1    //realtion between sets A and B
+    for b=1:1:N2
+      m(c,d)=i(a);
+      m(c,d+1)=j(b);
+      c=c+1;
+    end;
+end;
+disp(m);
\ No newline at end of file
diff --git a/48/CH2/EX2.5/eg_2_5.sce b/48/CH2/EX2.5/eg_2_5.sce
new file mode 100755
index 000000000..a43c42d09
--- /dev/null
+++ b/48/CH2/EX2.5/eg_2_5.sce
@@ -0,0 +1,61 @@
+clear;
+clc;
+//N=input("enter the no of elements in the set :");
+//for i=1:1:N
+//    s(1,i)=input("enter the elements in the set :");
+//end;
+//n=input("enter the number of pairs in the relation :");
+//for j=1:1:n
+//    for k=1:1:2
+//        r(j,k)=input("enter the elements in the relation :");
+//    end
+//end
+N=2;
+s=['a' 'b'];        //elements in the set
+n=3;
+r=['a' 'a';'b' 'b';'a' 'b'];    //realtion between the elements in the above set.
+ref=zeros(1,N);
+for a=1:1:N
+   for b=1:1:n
+      if(r(b,1)==s(1,a)&r(b,2)==s(1,a))
+           ref(1,a)=1;
+      end
+   end
+end
+for i=1:1:N        //checking whether above relation is reflexive or not
+    if(ref(1,i)==1)
+        disp("the above relation is reflexive with elements ");
+        disp(s(1,i));
+        disp(" ");
+    end
+end
+sym=zeros(1,(N*N-1)/2);
+s(1,N+1)=s(1,1);
+for a=1:1:N            //checking whether above relation is symmetric or not
+   for b=1:1:n
+      if(r(b,1)==s(1,a)&r(b,2)==s(1,a+1))
+          for d=1:1:n
+            if(r(d,1)==s(1,a+1)&r(d,2)==s(1,a))
+                sym(1,a)=1;
+                disp("the above relation is symmetric for these pairs :");
+                disp(")",s(1,a+1),s(1,a),"(");
+            end
+          end
+       end
+    end
+end
+for a=1:1:n            //checking whether it is transtive or not.
+    u=r(a,1);
+    v=r(a,2);
+        for b=a:1:n
+            if(r(b,1)==v)
+                w=r(b,2);
+                    for c=b:1:n
+                        if(r(c,1)==w&r(c,2)==u)
+                            disp("satisfies transtitve property");
+                            abort;
+                        end
+                    end
+            end
+        end
+end
\ No newline at end of file
diff --git a/48/CH2/EX2.6/eg_2_6.sce b/48/CH2/EX2.6/eg_2_6.sce
new file mode 100755
index 000000000..bc5faded8
--- /dev/null
+++ b/48/CH2/EX2.6/eg_2_6.sce
@@ -0,0 +1,34 @@
+clear;
+clc;
+//N=input("enter the elements in the set :");
+//for i=1:1:N
+//    s(i)=input("enter the elements :");
+//end
+N=2;
+s=['a' 'b'];
+disp("The equivalence relation of above set is :");
+h=1;
+for i=1:1:N        //to satisfy reflexive property
+    ref(h,1)=s(i);
+    ref(h,2)=s(i);
+    h=h+1;
+end
+for i=1:1:N        //to satisfy symmetric property
+    for j=i:1:N
+        if(i~=j)
+            ref(h,1)=s(i);
+            ref(h,2)=s(j);
+            h=h+1;
+        end
+    end
+end
+m=1;
+for i=1:max(size(ref(:,1)))        //to satisfy transtive property
+    if(ref(i,1)~=ref(i,2))
+        ref1(m,1)=ref(i,2);
+        ref1(m,2)=ref(i,1);
+        m=m+1;
+    end
+end
+disp(ref);
+disp(ref1);
\ No newline at end of file
diff --git a/48/CH2/EX2.7/eg_2_7.sce b/48/CH2/EX2.7/eg_2_7.sce
new file mode 100755
index 000000000..5977bd696
--- /dev/null
+++ b/48/CH2/EX2.7/eg_2_7.sce
@@ -0,0 +1,31 @@
+clc;
+clear;
+//n1=input("enter the no of elements in the 1st set");
+//for i=1:1:n1
+//    s1(i)=input("enter the elements of 1st set:");
+//end
+n1=3;
+s1=['a1' 'a2' 'a3'];        //set A
+//n2=input("enter the no of elements in the 2nd set");
+//for i=1:1:n2
+//    s2(i)=input("enter the elements of 2ns set:");
+//end
+n2=2;
+s1=['b1' 'b2'];        //set B
+//N=input("enter the pairs in the relation which you want to check whether is a function");
+//for i=1:1:N
+//    for j=1:1:2
+//       r(i,j)=input("enter the elements in the relation:");
+//    end
+//end
+N=3;
+r=['a1' 'b1';'a2' 'b2';'a2' 'b1'];        //Realtion r
+for i=1:1:N            //checks whether the relation is function or not
+    for j=i:1:N
+        if(r(i,1)==r(j,1) & i~=j)
+            disp("the relation is not a function");
+            abort;
+         end
+    end
+end
+disp("the realtion is a fucntion");
\ No newline at end of file
-- 
cgit