State whether each of the following statements are true or false. If the statement
is false, rewrite the given statement correctly.
(i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}.
(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered
pairs (x, y) such that x ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of
elements in (A×B).
If
2 5 1 1
3 3 3 3
x
,y – ,
+ = , find the values of x and y
If R is the set of all real numbers, what do the cartesian products R × R
and R × R × R represent?
Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find
(i) A × (B ∩ C) (ii) (A × B) ∩ (A × C)
(iii) A × (B ∪ C) (iv) (A × B) ∪ (A × C)
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