Question

If $p$ is any statement $t$ and $c$ are tautology and contradiction respectively, then which of the following is(are) correct?

• A. $p\wedge t\equiv p$
• B. $p\wedge c\equiv c$
• C. $p\vee t\equiv c$
• D. $p\vee c\equiv p$

Answer 1

Answer: (A), (B), (D)

$p\wedge t\equiv p$
$p\wedge c\equiv c$
$p\vee c\equiv p$

Tautology is the preposition which is always true and contradiction is a preposition which is always false.
Here $\wedge \equiv AND,\vee \equiv OR$, $T$=true and $F$=false
Given statement=$p$, tautology=$t$ and contradiction=$c$
a)$p\wedge t\equiv p$ irrespective of value of $p$ as $t=T$ always
And if $p=T$ then $T\wedge T=T$ and if $p=F$ then $F\wedge T=F$
Thus option (a) is correct.
b)$p\wedge c\equiv c$ irrespective of value of $p$ as$c=F$ always
And if $p=T$ then $T\wedge F=F$ and if $p=F$ then $F\wedge F=F$
Thus option (b) is correct
c)$p\vee t\equiv c$
If $p=T$ then $T\vee T\equiv T\ne c$ and if $p=F$ then $F\vee T\equiv T\ne c$
Thus option (c) is not correct
d)$p\vee c\equiv p$
If $p=T$ then $T\vee F\equiv T$ and if $p=F$ then $F\vee F\equiv F$
Thus it depends on the value of $p$
Hence option (d) is correct