Question

p: She is beautiful
q: She is intelligent
The symbolic representation of “She is neither beautiful nor intelligent” is
$A)\,p \wedge q \\\ B)\, \sim p \wedge q \\\ C)\,p \wedge ( \sim q) \\\ D)\,( \sim p) \wedge ( \sim q)$

Answer 1

The two statements are given in the questions. These statements given in the question are called logical statements p and q. In this case the required statement is to be represented in terms of logical operators operating on this statement. For that one needs to understand the logical operators.

Complete step-by-step solution:
In the question two statements are given
p: She is beautiful
q: She is intelligent
We need to find out the logical representation of statement “She is neither beautiful nor intelligent”
Negation or $\sim$ is used to denote ‘not this’ in the logical sense
And $\wedge$ is used for joining the two statements in a logical sense.
When one uses the logical operator ‘And’. Then the result is true only if both the statements are true.
Let us dissect the statement,
“She is neither beautiful nor intelligent”
First part of the statement is She is neither beautiful
In the question given statement ‘p’ is
p: She is beautiful
in this first part ‘p’ is denied she is not beautiful it can also be written as $\sim (p)$
similarly, second part of the sentence ‘nor beautiful’ refers denial of second statement i.e. ‘q’
q: She is intelligent
The denial can be represented as $\sim (q)$
When the whole statement Is joined both statements are true and can be joined by And operator
$\sim (p) \wedge \sim (q)$
Hence, option (D) is correct.

Note: In the case of logical representation of statement one needs to have command over operators and language of sentence, Language of sentence can play a big role in logical representation. One needs to understand how the sentence is delivered in order to get to the solution. Step by step approach is recommended.