Question

PLZZ GUYS CAN ANY ONE GIVE ANSWER FOR THESE QUESTIONS

Answer 1

Step-by-step explanation:

7)

Given:-

A={x:x is a perfect square number and x<50,x€N}

B={x:x=8m+1,m is a perfect square number and m is a perfect square,m€W,x<50,x€N}

To show:-

n(AUB)-n(AnB)=n(A-B)+n(B-A)

Solution:-

A={x:x is a perfect square and x<50 , x€N}

=>A={1,4,9,16,25,36,49}

B={x:x=8m+1,m is perfect square ,m€W,x<50,x€N}

=>B={1,9,33}

(AUB)={1,4,9,16,25,36,49}U{1,9,33}

=>AUB={1,4,9,16,25,33,36,49}

n(AUB)=8

AnB={1,4,9,16,25,36,49}n{1,9,33}A={1,9}

n(AnB)=2

A-B={1,4,9,16,25,36,49}-{1,9,33}

=>{4,16,25,36,49}

n(A-B)=5

B-A={1,9,33}-{1,4,9,16,25,36,49}

=>{33}

n(B-A)=1

Now,

n(AUB)-n(AnB)=8-2=6-----(1)

n(A-B)+n(B-A)=5+1=6------(2)

From (1)&(2)

n(AUB)-n(AnB)=n(A-B)+n(B-A)

Answer:-

n(AUB)-n(AnB)=n(A-B)+n(B-A)

8)

Given:-

A={x:x=2k+1,k€N,k≤5}

B={x:x is a composite number ,x<12}

To Show:-

(AUB)-(AnB)=(A-B)U(B-A)

Solution:-

A={x:x=2k+1,k€N,k≤5}

A={3,5,7,9,11}

B={x:x is a composite number ,x<12}

B={4,6,8,9,10}

AUB={3,5,7,9,11}U{4,6,8,9,10}

=>{3,4,5,6,7,8,9,10,11}

AnB={3,5,7,9,11}n{4,6,8,9,10}

=>{9}

A-B={3,5,7,9,11}-{4,6,8,9,10}

=>{3,5,7,11}

B-A={4,6,8,9,10}-{3,5,7,9,11}

=>{4,6,8,10}

now,

(AUB)-(AnB)={3,4,5,6,7,8,9,10,11}-{9}

AUB)-(AnB)={3,4,5,6,7,8,10,11}---------(1)

(A-B)U(B-A)={3,5,7,11}U{4,6,8,10}

A-B)U(B-A)={3,4,5,6,7,8,10,11}--------(2)

From (1)&(2)

(AUB)-(AnB)=(A-B)U(B-A)

Answer:-

(AUB)-(AnB)=(A-B)U(B-A)