Q.Check whether “Or” used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
t: you are wet when it rains or you are in a river.

Statement t: "You are wet when it rains or you are in a river."

Component statements:

p: "You are wet when it rains."

q: "You are wet when you are in a river."

Type of Or: A person standing in a river while it is raining would be wet due to both causes at once — the two conditions are not mutually exclusive, so this Or is inclusive.

Truth check: Both p and q are individually true statements of fact (rain makes you wet; being in a river makes you wet). Since "Or" ($\vee$) requires at least one component to be true, and here both are true, the compound statement $t = p \vee q$ is True.

Split the sentence at "or" into its two component claims. Check whether both components can be simultaneously true (inclusive) or are mutually exclusive (exclusive). Then apply the Or truth rule: true if at least one component is true.

• Assuming "or" is exclusive by default without checking whether the two causes of wetness can coexist.
• Not evaluating the individual truth of each component before combining them.