What is the negation of the statement A->(B v(or) C)?a.None of the mentionedb.~A ∧ B v Cc.A->B->Cd.A ∧ ~B ∧ ~C
Question
What is the negation of the statement A -> (B v C)?
a. None of the mentioned
b. ~A ∧ (B v C)
c. A -> B -> C
d. A ∧ ~B ∧ ~C
Solution
The negation of the statement A->(B v C) is d. A ∧ ~B ∧ ~C.
Here's the step by step explanation:
-
The given statement is A->(B v C). This is a conditional statement which means "if A then (B or C)".
-
The negation of a conditional statement is formed by keeping the first statement and negating the second. So, the negation of A->(B v C) would be A and not (B or C).
-
The negation of (B or C) is ~B and ~C according to De Morgan's laws.
-
Therefore, the negation of the statement A->(B v C) is A and not B and not C, which is option d. A ∧ ~B ∧ ~C.
Similar Questions
The statement (~P<->Q)∧~Q is true when?a.P: False Q: Falseb.P: True Q: Falsec.P: False Q: Trued.P: True Q: True
The logical connective "AND" is also known as:a.Conjunctionb.Disjunctionc.Negationd.Implication
The compound proposition "p AND q" is true only when:a.Either p or q is trueb.Both p and q are truec.Neither p nor q is trued.None of the above
12-13. From the choices given above, identify two special expressions in negation.
Which of the following logical statements is true? a. False |= True b. True |= False c. (A^B) |= (A<=>B) d. A<=>B |= AvB e. A<=>B |= -AvB
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.