Question

Choose the correct answer from the given options by solving the following question:
\[p:\] It is hot,
\[q:\] He wants water.
Then, the verbal meaning of \[p \to q\] is?
A. It is hot or he wants water.
B. It is hot and he wants water.
C. If it is hot, then he wants water.
D. If and only if it is hot, he wants water.

Answer 1

Hint: Infer the given propositions and the question. Take a look at the logical operator asked and write down the meaning of that operator in English terms combining the two propositions using the logical connector.

Complete step-by-step solution:
Given,
\[p:\] It is hot,
\[q:\] He wants water.
According to the logical reasoning, \[p \to q\] means, if \[p\], then \[q\].
That implies, according to the given two propositions, it is inferred that,
If it is hot then he wants water.

$\therefore $ The correct option is C.

Additional Information: In the given question, it is asked that the implication must be taken. Implication, according to logical reasoning is a relationship between two propositions in which the second implication is the consequence of the first proposition. It is broken down as “If \[A\], then \[B\]” in terms of the reasoning which in turn is read as “\[A\] implies \[B\]” and represented in symbolic form as \[A \to B\]

\[A\]	\[B\]	\[A \to B\]
\[T\]	\[T\]	\[T\]
\[T\]	\[F\]	\[F\]
\[F\]	\[T\]	\[T\]
\[F\]	\[F\]	\[T\]

The truth table of \[A \to B\] is as given below:
Here, the \[T\] represents True.
The \[F\] represents False.

Note: The logical implication is also known as a conditional statement. It is formed by joining two simple statements with the logical implication connective or operator. You prove the implication \[p \to q\] by assuming \[p\] is true and using your background knowledge and the rules of logic to prove \[q\] is true. The assumption “\[p\] is true” is the first link in a logical chain of statements, each implying its successor, that ends in “\[q\] is true.”