Question

Which of the following is true?

a. A-B =A ∩ B b. A-B=B-A

c. (A U B)’ =A’ U B’ d. (A ∩ B)’ =A’ U B’​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(a)A-B=A{\cap}B}$

$\mathsf{(b)A-B=B-A}$

$\mathsf{(c)(A{\cup}B)'=A'{\cup}B'}$

$\mathsf{(d)(A{\cap}B)'=A'{\cup}B'}$

$\underline{\textbf{To find:}}$

$\textsf{which of the given is correct}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\mathsf{1.\;A-B=A{\cap}B'}$

$\mathsf{2.\;A-B{\neq}B-A}$

$\mathsf{3.\;Demorgan's\;law}$

$\mathsf{(i)(A{\cup}B)'=A'{\cap}B'}$

$\mathsf{(ii)(A{\cap}B)'=A'{\cup}B'}$

$\mathsf{Consider,}$

$\mathsf{(a)A-B=A{\cap}B}\;\;\textbf{-Incorrect}\;\textsf{(by (1))}$

$\mathsf{(b)A-B=B-A}\;\;\textbf{-Incorrect}\;\textsf{(by (2))}$

$\mathsf{(c)(A{\cup}B)'=A'{\cup}B'}\;\;\textbf{-Incorrect}\;\textsf{(by 3(i))}$

$\mathsf{(d)(A{\cap}B)'=A'{\cup}B'}\;\;\textbf{-Correct}\;\textsf{(by 3(ii))}$