Not (A and B) is the same as Not A and Not B.Group startsTrue or FalseTrue, unselectedFalse, unselected
Question
Not (A and B) is the same as Not A and Not B.
Group starts
True or False
- True, unselected
- False, unselected
Solution
To answer the question, let's break it down step by step:
-
The statement "Not (A and B)" is equivalent to "Not A or Not B" according to De Morgan's laws.
-
The statement "Not A and Not B" means that both A and B are false.
-
In the given group, we have two options: True or False for A, and True or False for B.
-
If A is True and B is True, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.
-
If A is True and B is False, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.
-
If A is False and B is True, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.
-
If A is False and B is False, then "Not A and Not B" would be True and the statement "Not (A and B)" would also be True.
Therefore, the statement "Not (A and B)" is not always the same as "Not A and Not B". It is only equivalent when both A and B are False.
Similar Questions
If p → ( ¬p ∨ q) is false, then the truth values of p and q are respectively T, F.Group startsTrue or FalseTrue, unselectedFalse, unselected
The proposition p↔q is equivalent to (¬p ∨ q) ∧(¬q ∨ p) Group startsTrue or FalseTrue, unselectedFalse
The simplification of[ NOT(p AND q) AND (NOT p OR q) AND (NOT q OR q) ] AND pisQuestion 4Answera.T.b.F.c.q.d.NOT q.e.None of the Given Choices.f.p.g.NOT p.
Let A = {a ,b, c , d}, B = {b , d , e ,h}, then A⊕B = { a , c , h}Group startsTrue or FalseTrue, unselectedFalse, unselected
Either the left or right operand must be true describes the _____ Boolean operator. A. OR B. OPTIONAL C. NOT D. AND
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.