initial commit / add all books

10 files changed, 358 insertions, 0 deletions

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