Question

Cbse jee main and advance portion std 11

Answer 1

Answer: Here we can see that P×Q is not equal to Q×P

Step-by step solution:

Given: P={a, e, i} and Q={1, 3,5)

P×Q={(a, 1), (a, 3), (a,5), (e, 1), (e, 3), (e, 5), (i, 1), (i, 3), (i, 5) }

Q×P={(1, a), (1, e), (1, i), (3, a), (3, e), (3, i), (5, a), (5, e), (5, i) }

P×P={(a, a), (a, e), (a, i), (e, a), (e, e), (e, i), (i, a), (i, e), (i, i) }

Q×Q={(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5) }

Here, we can observe that these are Cartesian products.

The Cartesian products in sets theories is the multiplication of two or more than two sets resulting in a sets of their products. If there are two sets given P and Q then the Cartesian product of P×Q results in the set containing the ordered pair in which p€P and q€Q.