Q39 of 68 Page 27

State True or False for the following statements

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

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)}


More from this chapter

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37

Fill in the blanks:

Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}


g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}


be two real functions. Then Match the following :


 38

State True or False for the following statements

The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ Z}

 40

State True or False for the following statements

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C)


= {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.

 41

State True or False for the following statements

If (x – 2, y + 5) = are two equal ordered pairs, then x = 4, .