Question

Consider the following grammar.

$S\to ABA\to \left(S\right)|aSb|dB\to aB|\epsilon$

$IfX=First\left(S\right),Y=First\left(A\right)andZ=First\left(B\right)then(X\cap Y)-Z$ is_________.

• A. {(,d}
• B. $\left\{\epsilon \right\}$
• C. {(,a,d}
• D. {}

Answer 1

The correct option is A {(,d}

First(S) = First (A) = {(,a,d}
First (B) = $\{a,\epsilon \}$
$X\cup Y=\left\{\right(,a,d\}$
$(X\cap Y)-Z=\left\{\right(,a,d\}-\{a,\epsilon \}$
= {(,d}.