Question

if u =(1,2,3,4,5,6,7,8,9,10) , A=(2,4,6) B=(1,3,5) then find Ac and Bc and show them by venn diagram if someone answer in detail i will mark him brainilist​

Answer 1

Answer:

Given, A={1,2,3,4,5},B={2,4,6,8} and C={3,4,5,6}

For the LHS:

Union of two sets will have the elements of both sets.

So, B∪C={2,3,4,5,6,8}

A−(B∪C) will have elements of A which are not in (B∪C)

So, A−(B∪C)={1} ..... (1)

For the RHS:

A−B will have elements of A which are not in B.

So, A−B={1,3,5}

A−C will have elements of A which are not in C.

So, A−C={1,2}

Intersection of two sets has the common elements of both the sets.

⇒(A−B)∩(A−C)={1} ..... (2)

From (1) and (2), we have

A−(B∪C)=(A−B)∩(A−C)

Hence, the given expression is true...

THANK YOU...IT MAY HELP YOU...BUT BECAUSE THE EXPLANATION IS SO LONG THE DUAGRAM IS NOT COMING...

SORRY!...FOR THAT...THANK YOU AND BYE...

Answer 2

Answer:

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B)

′

=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}

=ϕ

A

′

∩B

′

=(U−A)n(U−B)

={3,4,6}n{1,2,7}

=ϕ

Hence (A∪B)

′

=A ′ ∩B ′ .