intersection

Consider the following two statements : $$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the $$\,\,\,\,\,\,\,\,\,...

Consider the language : $${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$ Which of t...

Let P(S) denote the power set of a set S. Which of the following is always true?

The relational algebra expression equivalent to the following tuple calculus expression: $$\left\{ {t|t \in r \wedge \left( {t\left[ A \right] = 10 \wedge t\left[ B \right] = 20} \...

If $${L_1}$$ is a context free language and $${L_2}$$ is a regular which of the following is/are false?

Let $${R_1}$$ and $${R_2}$$ be two equivalence relations on a set. Consider the following assertions: (i)$$\,\,\,\,{R_1} \cup {R_2}$$ is an euivalence relation (ii)$$\,\,\,\,{R_1}...

The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. That is the pr...

If $${L_1}$$ and $${L_2}$$ are context free languages and $$R$$ a regular set, one of the languages below is not necessarily a context free language. Which one?

Let $${G_1}$$ and $${G_2}$$ be subgroups of a group $$G$$. (a) Show that $${G_1}\, \cap \,{G_2}$$ is also a subgroup of $$G$$. (b) $${\rm I}$$s $${G_1}\, \cup \,{G_2}$$ always a su...

Given that language $${L_1}$$ is regular and that the language $${L_1} \cap {L_2}$$ is regular is the language $${L_2}$$ is always regular?

State whether the following statement is TRUE / FALSE. The intersection of two $$CFL's$$ is also $$CFL.$$