The simplification of(NOT p) OR (p AND q) OR [p AND (NOT(NOT p OR q))]isQuestion 13Answera.True.b.False.c.p.d.q.e.None of the Given Choices.

Sure, let's simplify the expression step by step:

Given expression: (NOT p) OR (p AND q) OR [p AND (NOT(NOT p OR q))]

1. Simplify the innermost part first: NOT(NOT p OR q)

   • Apply De Morgan's law: NOT(NOT p OR q) = (p AND NOT q)

2. Substitute back into the expression: (NOT p) OR (p AND q) OR [p AND (p AND NOT q)]

3. Simplify the term inside the brackets: p AND (p AND NOT q) = p AND p AND NOT q = p AND NOT q

4. Substitute back into the expression: (NOT p) OR (p AND q) OR (p AND NOT q)

5. Apply the distributive property: (NOT p) OR [(p AND q) OR (p AND NOT q)] = (NOT p) OR [p AND (q OR NOT q)]

6. Simplify inside the brackets: q OR NOT q is always true (a tautology), so: (NOT p) OR [p AND true] = (NOT p) OR p

7. Simplify the final expression: (NOT p) OR p is always true (a tautology).

Therefore, the simplification of the given expression is: a. True.