State True or False for the statement:If P = {1, 2}, then P × P × P

1.	State True or False for the statement:If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}
Answer» The given statement is false. Explanation: The set P = {1, 2} is given ⇒ n(P) = 2 Now we need to find P×P×P, So number of elements in P×P×P, will be n(P×P×P) = n(P)×n(P)×n(P) = 2× 2× 2 = 8 But given P×P×P set has just 4 elements; hence it is not the set of P×P×P. The set of P×P×P is P×P×P = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}

State True or False for the statement:If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}

Answer»

The given statement is false.

Explanation:

The set P = {1, 2} is given

⇒ n(P) = 2

Now we need to find P×P×P,

So number of elements in P×P×P, will be

n(P×P×P) = n(P)×n(P)×n(P) = 2× 2× 2 = 8

But given P×P×P set has just 4 elements; hence it is not the set of P×P×P.

The set of P×P×P is

P×P×P = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}