Question

Which of the following is(are) incorrect for the statement $p$ and $q$ ?

• A. $p\wedge q$ is true when atleast one from $p$ and $q$ is true.
• B. $p\to q$ is true when $p$ is true and $q$ is false.
• C. $p\leftrightarrow q$ is true only when both $p$ and $q$ are true.
• D. None of these.

Answer 1

Answer: (A), (B), (C)

The correct options are
A $p\wedge q$ is true when atleast one from $p$ and $q$ is true.
B $p\to q$ is true when $p$ is true and $q$ is false.
C $p\leftrightarrow q$ is true only when both $p$ and $q$ are true.

A) p q is true only when both p and q are true so option (A)
is incorrect.
(B) we know that p q is false only when p is true and q is
false so (B) is incorrect.
(C) is incorrect since p q is true only when either p and q
both are true or both are false