If p is true, q is false, and r is true, what is the truth value of r∨(q∧~p)?truefalsecannot be determinedSubmit
Question
If p is true, q is false, and r is true, what is the truth value of r ∨ (q ∧ ~p)?
true
false
cannot be determined
Solution
The truth value of r∨(q∧~p) can be determined as follows:
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Substitute the given values into the expression: r∨(q∧~p) becomes true ∨ (false ∧ ~true).
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Evaluate the negation: ~true becomes false, so the expression becomes true ∨ (false ∧ false).
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Evaluate the conjunction: false ∧ false becomes false, so the expression becomes true ∨ false.
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Evaluate the disjunction: true ∨ false becomes true.
So, the truth value of r∨(q∧~p) is true.
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