Question

which of the following options best completes the column for!(x || x) || (!x &&!y) in the truth table? x y!(x || x)!x &&!y!(x || x) || (!x &&!y) t t ? t f f t f f

Explanation:

Step1: Calculate \(!(x||x)\)

When \(x = T\), \(x||x=T\), so \(!(x||x)=F\). When \(x = F\), \(x||x=F\), so \(!(x||x)=T\).

Step2: Calculate \(!x\&\&!y\)

When \(x = T,y = T\), \(!x = F,!y = F\), so \(!x\&\&!y=F\). When \(x = T,y = F\), \(!x = F,!y = T\), so \(!x\&\&!y=F\). When \(x = F,y = T\), \(!x = T,!y = F\), so \(!x\&\&!y=F\). When \(x = F,y = F\), \(!x = T,!y = T\), so \(!x\&\&!y=T\).

Step3: Calculate \(!(x||x)||(!x\&\&!y)\)

When \(x = T,y = T\): \(F||F=F\). When \(x = T,y = F\): \(F||F=F\). When \(x = F,y = T\): \(T||F=T\). When \(x = F,y = F\): \(T||T=T\).

Answer:

\(x\)	\(y\)	\(!(x		x)\)	\(!x\&\&!y\)	\(!(x		x)		(!x\&\&!y)\)
\(T\)	\(F\)	\(F\)	\(F\)	\(F\)
\(F\)	\(T\)	\(T\)	\(F\)	\(T\)
\(F\)	\(F\)	\(T\)	\(T\)	\(T\)