Complement of the expression A’B + CD’ is _________a)(A’ + B)(C’ + D)b)(A + B’)(C’ + D)c)(A + B’)(C + D’)d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Complement of the expression A&rsquo;B + CD&rsquo; is _________a)(A&rsquo; + B)(C&rsquo; + D)b)(A + B&rsquo;)(C&rsquo; + D)c)(A + B&rsquo;)(C + D&rsquo;)d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Answer

The complement of the expression A is the opposite of A. It is everything that is not included in A. In set theory, the complement of a set A is denoted by A'. For example, if A is the set of all even numbers less than 10, then A' is the set of all odd numbers less than 10. Similarly, if A is the set of all people who own a car, then A' is the set of all people who do not own a car.

Answer

(A’B + CD’)’ = (A’B)'(CD’)’ (By DeMorgan’s Theorem) = (A” + B’)(C’ + D”) (By DeMorgan’s Theorem) = (A + B’)(C’ + D).

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