Question

Which of the following is a tautology

• A. $a\vee b\to b\wedge c$
• B. $a\wedge b\to b\vee c$
• C. $a\vee b\to (b\to c)$
• D. Both $\left(a\right)$ and $\left(c\right)$ are true

Answer 1

The correct option is B $a\wedge b\to b\vee c$

$\begin{array}{ccccccccccc}a& b& c& a\vee b& a\wedge b& b\vee c& b\wedge c& b\to c& a\vee b\to b\wedge c& a\wedge b\to (b\vee c)& (a\vee b)\to (b\to c)\\ T& T& T& T& T& T& T& T& T& T& T\\ T& T& F& T& T& T& F& F& T& T& F\\ T& F& T& T& F& T& F& T& T& T& T\\ T& F& F& T& F& F& F& T& F& T& T\\ F& T& T& T& F& T& T& T& T& T& T\\ F& T& F& T& F& T& F& F& T& T& F\\ F& F& T& F& F& T& F& T& T& T& T\\ F& F& F& F& F& F& F& T& T& T& T\end{array}$

From the above truth table, it is clearly evident that only the preposition $a\wedge b\to b\vee c$ has all the truth value true. Hence it is a tautology.