Question

If \[p:\] “2 plus 3 is 5” and \[q:\] “Delhi is the capital of India” are two statements. Then what is the logical representation of the statement “Delhi is the capital of India and it is not that 2 plus 3 is 5”?
A. \[\sim p \vee q\]
B. \[\sim p \wedge q\]
C. \[p \wedge \sim q\]
D. \[p \vee \sim q\]
E. \[\sim p \wedge \sim q\]

Answer 1

Hint In the given question, two statements are given. First, find the meaning of mathematical logical symbols present in the given statement. Then convert the statement into the required logical representation.

Formula used
Meaning of logical symbols are:
\[\sim :\] Negation
\[ \wedge :\] And

Complete step by step solution:
The given statements are:
  \[p:\]“2 plus 3 is 5”
  \[q:\]“Delhi is the capital of India”
Delhi is the capital of India and it is not that 2 plus 3 is 5
In mathematical logic, “not” represent the negation and “and” is represented by the symbol \[ \wedge \].
Therefore, the logical representation of the statement “Delhi is the capital of India and it is not that 2 plus 3 is 5” is:
\[q \wedge \sim p\]
\[ \Rightarrow \]\[\sim p \wedge q\]
Hence the correct option is B.

Note: Students often confused with the sign \[ \wedge \] and \[ \vee \].
Meaning of \[p \wedge q\] is \[\left( {p and q} \right)\].
Meaning of \[p \vee q\] is \[\left( {p or q} \right)\].