List of top Mathematics Questions on Statements asked in KEAM

Which of the following sentences is/are statement(s)?
(i) 10 is less than 5.
(ii) All rational numbers are real numbers.
(iii) Today is a sunny day.

If \( p : 3 \) is a prime number and \( q : \text{one plus one is three} \), then the compound statement “It is not that 3 is a prime number or it is not that one plus one is three” is:

Let \( p : 57 \) is an odd prime number,
\( q : 4 \) is a divisor of 12,
\( r : 15 \) is the LCM of 3 and 5 be three simple logical statements.
Which one of the following is true?

Consider the two statements \(P\): He is intelligent and \(Q\): He is strong. Then the symbolic form of the statement “It is not true that he is either intelligent or strong” is