Which one of the following Boolean expressions is a tautology?

Options

A. `(p vee q) vee (p vee ~ q)`
B. `(p wedge q) vee (p wedge ~ q)`
C. `(p vee q) wedge (p vee ~ q)`
D. `(p vee q) wedge (p vee ~ q)`

Answer

A

Explanation

Option (a) `(p vee q) vee (p vee (~q))`
`-= p vee (qv ~ q)` is tautolgy,
` [ because q vee (~q) -= T and p vee T -= T]`
Option (b)
`(p vee q) vee (p wedge (~q))-= p wedge (q vee ~ q)`
not a tautology,
`[ because q vee ~ q-= T and p wedge T -= p]`
Option (c)
`(p vee q) wedge (p vee (~q)) -= p vee (q wedge ~q)`
not a tautology `[ because q wedge ~q-= F and p vee F-= p]`
Option (d)
`(p vee q) wedge ((~p) vee (~q))-= (p vee q) wedge ( ~ (p wedge q))`
not a tautology.