The truth value of the proposition "p OR q" is true if:a.Both p and q are trueb.Either p or q is truec.Neither p nor q is trued.Both p and q are false

To determine the truth value of the proposition "p OR q," let's analyze the options provided:

1. Both p and q are true: In this case, "p OR q" is true, as at least one of the propositions (in this case, both) is true.

2. Either p or q is true: This is the precise definition of the logical OR operation. If at least one of the two propositions (p or q) is true, then "p OR q" is true.

3. Neither p nor q are true: If both p and q are false, then "p OR q" is false, which contradicts the proposition.

4. Both p and q are false: Similar to the previous rationale, if both propositions are false, then "p OR q" is also false.

Based on the analysis above, the correct choice is:

Final Answer

b. Either p or q is true