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प्रश्न
If P = {x : 3x + 4 ≤ 23, x ∈ N} and Q = {x : −6 ≤ 2x + 2 < 9, x ∈ I} find PQ.
योग
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उत्तर
PQ = P ∩ Q
Find set P
P = {x : 3x + 4 ≤ 23, x ∈ N}
3x ≤ 19
`x <= 19/3`
= 6.33
Since x ∈ N = {1, 2, 3, …},
P = {1, 2, 3, 4, 5, 6}
Find set Q
Q = {x : −6 ≤ 2x + 2 < 9, x ∈ I}
−6 ≤ 2x + 2 < 9
−8 ≤ 2x < 7
−4 ≤ x < 3.5
Q = {−4, −3, −2, −1, 0, 1, 2, 3}
Find PQ = P ∩ Q
P = {1, 2, 3, 4, 5, 6}
Q = {−4, −3, −2, −1, 0, 1, 2, 3}
PQ = {1, 2, 3}
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