Write the following statement in the form of "if-then":
The banana trees will bloom if it stays warm for a month.

The simplified switching circuit for the following circuit is (Assume the circuit consists of two switches $S_1$ and $S_2$ in parallel, connected in series with a switch $S_3$):

The symbolic form of the given switching circuit is equivalent to $..........$

Check the validity of the statement given below by the method specified against it.
$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...

Negation of the statement "The payment will be made if and only if the work is finished in time." is