Mathematics
Let P = {x : x is a factor of 18} and Q = {x : x is a factor of 24}.
(i) Write each one of P and Q in Roster form.
(ii) Find:
(a) P ∪ Q
(b) P ∩ Q
Answer
(i) Write each one of P and Q in Roster form.
P = {x : x is a factor of 18}
Factors of 18 are numbers that divide 18 exactly: 1, 2, 3, 6, 9, 18.
P = {1, 2, 3, 6, 9, 18}
And
Q = {x : x is a factor of 24}
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
Q = {1, 2, 3, 4, 6, 8, 12, 24}
∴ P = {1, 2, 3, 6, 9, 18}, Q = {1, 2, 3, 4, 6, 8, 12, 24}
(ii) Find:
(a) P ∪ Q
P = {1, 2, 3, 6, 9, 18}
Q = {1, 2, 3, 4, 6, 8, 12, 24}
P ∪ Q = {1, 2, 3, 6, 9, 18} ∪ {1, 2, 3, 4, 6, 8, 12, 24}
∴ P ∪ Q = {1, 2, 3, 4, 6, 8, 9, 12, 18, 24}
(b) P ∩ Q
P = {1, 2, 3, 6, 9, 18}
Q = {1, 2, 3, 4, 6, 8, 12, 24}
P ∩ Q = {1, 2, 3, 6, 9, 18} ∩ {1, 2, 3, 4, 6, 8, 12, 24}
∴ P ∩ Q = {1, 2, 3, 6}
Related Questions
Suggest a universal set for the sets given below :
(i) {5, 7, 9}, {3, 5, 7}, {1, 3, 9} and {2, 4, 8}.
(ii) {odd numbers less than 8}, {prime numbers less than 8} and {even numbers between 3 and 8}.
(iii) {vowels in English alphabet}, {consonants in English alphabet}.
Let A = {2, 4, 6, 8}, B = {6, 8, 10, 12} and C = {7, 8, 9, 10}. Find :
(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) A ∩ B
(v) A ∩ C
(vi) B ∩ C
Let A = {a, b, c}, B = {b, d, e} and C = {e, f, g}, verify that :
(i) A ∪ B = B ∪ A
(ii) (A ∪ B) ∪ C = A ∪ (B ∪ C)
(iii) A ∩ B = B ∩ A
(iv) (A ∩ B) ∩ C = A ∩ (B ∩ C)
Let A = {x : x is a multiple of 2, x < 15}, B = {x : x is a multiple of 3, x < 20}, C = {x : x is a prime, x < 20}.
(i) Write each one of the sets A, B, C in Roster form.
(ii) Find:
(a) A ∪ B
(b) A ∪ C
(c) B ∪ C
(d) A ∩ B
(e) A ∩ C
(f) B ∩ C