Today our topic of discussion is Sets and Functions Exercises 2.1.
Sets and Functions Exercises 2.1
Exercises 2.1
- Express the following sets in set builder notation:
1) {x ∈ N :(x²) > 9 and * x³ < 130 }
2) { x ∈Z :(x²) > 5and * x³ <= 36 }
3) {x ∈N : x is factor of 36 and z is a multiple of 6}
4){x ∈N :(x³) > 25 and * x ^ 4 < 264 }
- Express the following sets in set builder notation:
1) {3, 5, 7, 9, 11}
2) {1, 2, 3, 4, 6, 9, 12, 18, 36}
3) {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}
4) {pm 4 , pm5, pm6}
- If A = {2, 3, 4} , B = {1, 2, a} and C = {2, a, b} then determine the following sets:
1) B \ C
2) A ∪ B
3) A ∩ C
4) A ∪ (B ∩ C) 5) A ∩ (B ∩ C)
- If U = {1, 2, 3, 4, 5, 6, 7} A = {1, 3, 5} B = {2, 4, 6} and C = {3, 4, 5, 6, 7} verify the following statements:
1) (A ∪B)’ = A’ ∩ B’
2) (B ∩ C)’= B’ ∪ C’
3) ( A ∪B) ∩C=(A ∩ C) ∪(B ∩ C)
4) ( A ∩ B) ∪C=(A ∪C) ∩(B ∪C)
- If Q = {x, y} and R = \{m, n, l} then determine P(Q) and P(R)
- If A = {a, b} , B = {a, b, c} and C =A cup B then show that number of elements of P(C) is 2″, where n is the number of elements of C.
- 1) If (x – 1, y + 2) = (y – 2, 2x + 1) then determine r and y.
2) If (ax – cy, a ²- c ²) = (0, ay – cx) then determine (x, y).
3) If (6x – y, 13) = (1, 3x + 2y) then determine (x,y).
- 1) If P = {a}, Q = {b, c} then determine PQ and QP
2) If A = {3, 4, 5} B = {4, 5, 6 } and C = {x, y} determine ( A ∩ B)* C
3) If P = {3, 5, 7} , Q ={ 5 7}and R =P \Q determine (P ∪ Q )* R.
- If A and B are respectively sets of all factors of 35 and 45, then determine AUB and AnB.
- Determine the natural numbers that divide both 346 and 556 to have 31 as residue.
- Of the 30 students of a class 20 like football and 15 cricket. Number of students who like both the games is 10. Determine using Venn diagram the number of students who do not like either of the games.
- Of 100 students 65 passed in Bangla, 48 in both Bangla and English and 15 failed in both the subjects.
1) Express the above in Venn diagram along with brief description.
2) Determine the number of students who passed only in Bangla or passed only in English.
3) Determine union of the sets of prime factors of number of students passed and failed in both the subjects.
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