not sure if possible to ask like this , but im trying my luck
Answers
1. List the members of ({, , , }). Which are proper subsets of {, , , }?
2. If has 10 members, how many members does () have?
3. In the following, what relation must hold between sets and in order for the given condition to be true?
a) ∩ = b) ∪ = c) ( ∩ )′ = ′
4. The symmetric difference of two sets and is the set
∆ = ( ∪ ) − ( ∩ )
If = {1, 2, 3} and = {2, 3, 4, 5}, find ∆ .
5. Justify the following statement or else give an example to disprove the result. Let
and be subsets of a set .
( − )′ = ( − )′
6. Let = {, , , , , , }, = {, , }, = {, }, and = {, , } be sets, where
acts as the universal set. Determine the following sets.
a) × b) × c) × d) × ×
7. In an examination, 70% of the candidates passed in mathematics, 73% passed in physics, and 64% passed in both subjects. If 63 candidates failed in both subjects, use a Venn diagram to find the total number of candidates who appeared at the examination.
8. Prove that the function () = 2 + 1 from the set of positive integers to the set of positive integers is one-to-one.
9. Prove that the function () = 2 − 2 from the set of positive integers to the set of integers is not one-to-one.
10. Prove that the function () = 2 − 1 from the set of positive integers (ℕ) to the set of positive integers is not onto ℕ.
1. List the members of ({, , , }). Which are proper subsets of {, , , }?
2. If has 10 members, how many members does () have?
3. In the following, what relation must hold between sets and in order for the given condition to be true?
a) ∩ = b) ∪ = c) ( ∩ )′ = ′
4. The symmetric difference of two sets and is the set
∆ = ( ∪ ) − ( ∩ )
If = {1, 2, 3} and = {2, 3, 4, 5}, find ∆ .
5. Justify the following statement or else give an example to disprove the result. Let
and be subsets of a set .
( − )′ = ( − )′
6. Let = {, , , , , , }, = {, , }, = {, }, and = {, , } be sets, where
acts as the universal set. Determine the following sets.
a) × b) × c) × d) × ×
7. In an examination, 70% of the candidates passed in mathematics, 73% passed in physics, and 64% passed in both subjects. If 63 candidates failed in both subjects, use a Venn diagram to find the total number of candidates who appeared at the examination.
8. Prove that the function () = 2 + 1 from the set of positive integers to the set of positive integers is one-to-one.
9. Prove that the function () = 2 − 2 from the set of positive integers to the set of integers is not one-to-one.
10. Prove that the function () = 2 − 1 from the set of positive integers (ℕ) to the set of positive integers is not onto ℕ.