Mathematical Reasoning MCQ Questions & Answers in Algebra | Maths
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61.
If $$p \Rightarrow \left( {q \vee r} \right)$$ is false, then the truth values of $$p, q, r$$ are respectively
A
$$T , F , F$$
B
$$F , F , F$$
C
$$F , T , T$$
D
$$T , T , F$$
Answer :
$$T , F , F$$
$${p \Rightarrow q}$$ is false only when $$p$$ is true and $$q$$ is false.
$${\therefore p \Rightarrow q}$$ is false when $$p$$ is true and $${p \vee r}$$ is false, and $${q \vee r}$$ is false when both $$q$$ and $$r$$ are false.
62.
Negation of "Paris in France and London is in England" is
A
Paris is in England and London is in France
B
Paris is not in France or London is not in England
C
Paris is in England or London is in France
D
None of these
Answer :
Paris is not in France or London is not in England
Let $$p :$$ Paris is in France, $$q :$$ London is in England
$$\therefore $$ we have $${p \wedge q}$$
Its negation is $$ \sim \left( {p \wedge q} \right) = \,\, \sim p \vee \sim q$$
i.e., Paris is not in France or London is not in England.