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Which one of the following statement is not a tautology?A. `(p wedge q) to (~ p ) vee q`B. `(p wedge q) to p`C. `p to (p vee q)`D. ` (p vee q) to (p vee (~q))` |
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Answer» Correct Answer - D `(p wedge q) to (~p) vee q` `-= (~(p wedge q)) vee ((~p) vee q)` ` -= ((~p) vee (~q)) vee ((~p) vee q)` `-=(~p) vee (~q) vee q " "[ because (~p) vee (~p) -= ~p]` ` -= (~p) vee T " "[because ~q vee q -= T]` `-= T` So, it is a tautology `" " [ because (( ~q) vee q) " is tautology"]` (b) `(p wedge q) to p -= (p wedge q) vee p` `-= (( ~p) vee (~q)) vee p` ` " "[ because ~ (p wedge q) -= (~p) vee (~q)]` `-= (~ p vee p ) vee (~q)` is tautology. ` [ because ~ p vee p " is a tautology and " (~q) vee T -= T]` (c) `because p to (p vee q) -= (~p) vee (p vee q)` `[ because p to q " is equivalent and " (~p vee q)]` `-= (~p vee p ) vee q` is tautology. `[ because (~p vee p) " is tautology and " q vee T -= T]` (d) `(p vee q) to (p vee (~q))` `-= (~(p vee q)) vee (p vee (~q))` `-= ((~p) wedge (~q)) vee (p vee (~q))` `-= (p vee (~q) vee ((~p ) wedge (~q))` `-= (p vee (~q) vee (~p)) wedge (p vee (~q) vee (~q))` `-= (T vee (~q)) wedge (p wedge (~q))` `-= T wedge (p wedge (~q))` `-= p wedge (~q),` which is not a tautology. |
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