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 subgroup of $$G$$?

Prove that in a finite graph, the number of vertices of odd degree is always even.

How many minimum spanning tress does the following graph have? Draw them (Weights are assigned to the edges).

If the proposition $$\neg p \Rightarrow q$$ is true, then the truth value of the proposition $$\neg p \vee \left( {p \Rightarrow q} \right)$$ where $$'\neg '$$ is negation, $$' \vee '$$ is inclusive or and $$' \Rightarrow '$$ is implication, is