Question

Given A = {great}, B = {grand, ε}, and C = {mother, father}.

1. What is BC?

2. What is ABC?

3. What is A*BC?

Answer 1

Here we have to concatenate each set with another set.

Note: Concatenating any string with ε gives the original string only.

i)

B={grand,ε} and C={mother,father}

Now BC={grandmother,grandfather,mother,father} Here BC is nothing but concatenating B with C.

so BC = {grandmother,grandfather,mother,father}

In above example we are taking each string of B and Concatenating with Each string of C.

ii)

ABC Value

First concatenate A with B and then Concatenate with C

AB={great}{grand,ε}={greatgrand,great}

Now Concatenate AB with C

ABC={greatgrand,great}{mother,father}={greatgrandmother,greatgrandfather,greatmother,greatfather}

so ABC={greadgrandmother,greatgrandfather,greatmother,greatfather}

iii)

A*BC

Here A* means Kleen Closure

So A* can be written as A^0 U A^1 U A^2...

so when we put 0 in place of * we will get A^0={ε} and then concatenate with BC

i.e ={ε}{BC}={ε}{grandmother,grandfather,mother,father}

Similarly if we put 1 in place of * we will get ABC i.e ={greatgrandmother,greatgrandfather,greatmother,greatfather}

If we put 2 in place of * then we will get A^2 nothing but AA={great}{great}={greatgreat}

and then concatenate with BC.

{greatgreat}BC={greatgreat}{grandmother,grandfather,mother,father}={greatgreatgrandmother,greatgreatgrandfather,greatgreatmother,greatgreatfather}

So A^2BC={greatgreatgrandmother,greatgreatgrandfather,greatgreatmother,greatgreatfather}

Note: if you have any queries please post a comment thanks a lot...always available to help you...