Question

If A ={1, 2}, B={3, 4}, then A x $B \cap \emptyset$) = $\emptyset$. State whether the statement is True (or) False And Justify it

Answer 1

given, A = {1, 2} and B = {3, 4}
so, number of elements in A , n(A) = 2
and number of elements in B , n(B) = 2

now, number of elements in A × B = n(A) × n(B)
= 2 × 2 = 4

and A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}
but we know, empty set is the set which doesn't have element. e.g., $\emptyset=\{\}$
so, there is no any common member of $A\times B$ and $\emptyset$.

hence, $A\times B\cap\emptyset=\emptyset$

hence the given statement is true .

Answer 2

Answer:

True

Step-by-step explanation:

It is given that A = { 1,2 },

B = { 3,4 }

A × ( B∩∅)

= A × ( { 3 , 4 } ∩ { } )

= A × { }

= { 1 , 2 } × { }

= { }

= ∅

∴ A × ( B ∩ ∅ ) = ∅

.....