Question

P= {x:4≤x≤ 5, xe N} and Q = {x: 7<X>10,€N} then find p×q and q×p and show that p×q is not equal to q×p​

Answer 1

Answer : The sets P and Q are defined as follows:

P = {x : 4 ≤ x ≤ 5, x ∈ N} Q = {x : 7 < x < 10, x ∈ N}

For set P, the natural numbers (N) that satisfy the condition are {4, 5}. For set Q, the natural numbers that satisfy the condition are {8, 9}.

The Cartesian product of two sets A and B, denoted A×B, is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B.

Therefore,

P×Q = {(4,8), (4,9), (5,8), (5,9)} Q×P = {(8,4), (8,5), (9,4), (9,5)}

As you can see, P×Q is not equal to Q×P. This shows that the Cartesian product is not commutative.