If $$A = \left[ {\matrix{ 1 & 0 & 0 & 1 \cr 0 & { - 1} & 0 & { - 1} \cr 0 & 0 & i & i \cr 0 & 0 & 0 & { - i} \cr } } \right]$$ the matrix $${A^4},$$
calculated by the use of Cayley - Hamilton theoram (or) otherwise is

Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is

Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then

Show that proposition $$C$$ is a logical consequence of the formula $$A \wedge \left( {A \to \left( {B \vee C} \right) \wedge \left( {B \to \sim A} \right)} \right)$$ using truth tables.