(a) If a language A is {a} and another language B is {,1}, what is A.B³?

1. A.B³ = {a, a1, a11, a111}
2. A.B³ = {, a, a1, a2, a3}
3. A.B³ = {a, 1, 11, 111, 2, 3}
4. A.B³= {a, , 1, 11, 111}

(b) If A = {, a} and B = {a ,b}, what is (B²) (A.B)? ( means intersection)

1. {, a, b, aa, ab, bb, ba}
2. {, a, aa, ab}
3. {ab, ba}
4. {aa, ab}

(c) If A and B are languages with m and n strings respectively does it follow that A.B has mn strings? ("mn" means "m times n")

1. No, it is not true because at least there is a counter example, A = B = {, a}.
2. No, it is not true when both A and B are empty set
3. No, it is not true when A = B.
4. Yes.

(d) How many of the following languages can be defined by Finite Automata?

{ab, aabb, aaabbb, aaaabbbb, aaaaabbbbb....}

{abb, aabbbb, aaabbbbbb, aaaabbbbbbbb, ......}

{a, aa, aba, abba, abbba, abbbba, abbbbba, ......}

{a, bab, bbabb, bbbabbb, bbbbabbbb, ......}

1. 1
2. 2
3. 3
4. 4

(e) If A = {a,b} and B = {b,c}, what is A B and what is B A?

("" means difference, ref Formula Booklet)

1. A B = {a,b} and B A = {b,c}
2. A B = {b} and = B A = {b}
3. A B = {c} and = B A = {a}
4. A B = {a} and = B A = {c}

(f) A computer program which tells you the time returns different results at different times. Does this mean that it is non-deterministic?

1. Yes, it is non-deterministic.
2. Yes or no, it is non-deterministic because the results is different; but it is deterministic because it returns the correct time.
3. No, it is deterministic because the program performs the exact same operation.
4. No, it is deterministic because for any given time (i.e. for the same input) the result is same.