R supports Boolean operations & and && $($logical AND$),$ and $($II$)($logical OR$),($I$)$ NOT $($logical negation$)$ and, $($function for XOR, exclusive OR$).$ The shorter forms $($ & and $(1)$ perform comparisons element by element as the arithmetic operations do$.$ The longer forms $($&& and $(11)$ evaluate left to right looking only at the first element of each vector; evaluation proceeds only until the result is determined.

If a and $b$ are two logical vectors the

length $(x$&$y_0)$

is equal to