Let r \[\in\] {p, q, \[\sim\]p, \[\sim\]q} be such that the logical statement
r \[\vee\] (\[\sim\]p) \[\Rightarrow\] (p \[\wedge\] q) \[\vee\] r
is a tautology. Then r is equal to :
Solutions · 1
Official solution
Clearly r must be equal to \[\sim\] p
\[\because\] \[\sim\] p \[\vee\] \[\sim\] p = \[\sim\] p
and (p \[\wedge\] q) \[\vee\] \[\sim\] p = p
\[\therefore\] \[\sim\] p \[\Rightarrow\] p = tautology.