If T₁ = {x : x ∈ ℕ, x < 10, and both x and 10 − x are prime}, what is T₁?
Advertisement
Answer and explanation
Correct answer: T₁ = {3, 5, 7}
Test natural numbers less than 10 against both prime conditions. For x = 3, 10 − x = 7, and both are prime. For x = 5, 10 − x = 5, so both are prime. For x = 7, 10 − x = 3, and both are prime. The other natural numbers below 10 fail at least one condition, so T₁ = {3, 5, 7}.
Frequently asked questions
What is the correct answer to this question?
T₁ = {3, 5, 7}
Why is this the correct answer?
Test natural numbers less than 10 against both prime conditions. For x = 3, 10 − x = 7, and both are prime. For x = 5, 10 − x = 5, so both are prime. For x = 7, 10 − x = 3, and both are prime. The other natural numbers below 10 fail at least one condition, so T₁ = {3, 5, 7}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement