GATE Overflow Test Series | Mixed Subjects | Test 3 | Question: 2

Question

The regular expression for the language which have strings, starting and ending with different symbol, over $\Sigma = \{a,b\}$ is given by _______ (Mark all the appropriate choices)

• A. $a(a+b)^{\ast}b + b(a+b)^{\ast}b$
• B. $a(a+b)^{\ast}b + a(a+b)^{\ast}a$
• C. $b(a+b)^{\ast}a + a(a+b)^{\ast}a$
• D. $a(a+b)^{\ast}b + b(a+b)^{\ast}a$

Answer 1

Given that, $\Sigma = \{a,b\}$

$L = \{ab,ba,aaab,bbba,\dots\}$

Now, regular expression $RE = a(a+b)^{\ast}b + b(a+b)^{\ast}a$

So, the correct answer is $(D).$