Discrete Mathematics Thegatebook

Question

If $A=\phi$   then $A\times B =\phi?$
I mean $A$ is a null set or empty set

Comments

If you mean A $\times$ $\phi$ = $\phi$ then yes it is correct .

Answer 1

Cartesian product of two set A and B is given as:

 AxB = { (a,b) | a$\epsilon$A $\Lambda$ b$\epsilon$B }

Now we have A as empty set and B as the non-empty set. therefore there is no element a such that a$\epsilon$A satisfies, due to which the condition a$\epsilon$A $\Lambda$ b$\epsilon$B fails.

so we can conclude that AxB would also be an empty set.