Question

Let p: Mathematics is interesting and Let q: Mathematics is difficult then the symbol $p \wedge q$ means
A) Mathematics is interesting implies that Mathematics is difficult
B) Mathematics is interesting implies and is implied by Mathematics is difficult
C) Mathematics is interesting and Mathematics is difficult
D) Mathematics is interesting or Mathematics is difficult

Answer 1

Hint : $p \wedge q$ has a logical operator Ʌ which is also called logical conjunction which is used to combine two propositions to result another. Here combine the propositions p and q using and.

Complete step-by-step answer :
Briefly a mathematical statement is a sentence which is either true or false. It may contain words and symbols. For example ``The square root of 4 is 5" is a mathematical statement (which is, of course, false).
We are given that a proposition p: Mathematics is interesting and a proposition q: Mathematics is difficult.
$p \wedge q$ tells that p and q are combined using a logical operator Ʌ, which is a conjunction; if all the premises are true, the conclusion must be true.
So, join the propositions p and q using ‘and’.
p: Mathematics is interesting
q: Mathematics is difficult
$p \wedge q$ : Mathematics is interesting and Mathematics is difficult.
Therefore, from among the options given in the question Option C is correct.
So, the correct answer is “Option C”.

Note : $p \wedge q$ is a conjunction which is also read as ‘p and q’, $p \vee q$ is a disjunction which is also read as ‘p or q’, $p \to q$ is an implication which is also read as ‘if p then q’.