Which of the following statements is a tautology?
A. \((p\wedge q)\rightarrow p\)
B. \(p\rightarrow(p\wedge q)\)
C. \(p\wedge\sim p\)
D. \((p\vee q)\rightarrow p\)
A. \((p\wedge q)\rightarrow p\)
B. \(p\rightarrow(p\wedge q)\)
C. \(p\wedge\sim p\)
D. \((p\vee q)\rightarrow p\)
Best answer
Answer: A. \((p\wedge q)\rightarrow p\)
If \(p\wedge q\) is true then \(p\) is true, so the implication is always true. The others fail for (T,F), (F,T) and always, respectively.
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