If the singleton sets {2a + 1} and {7} are equal, what is the value of a?
Answer and explanation
Correct answer: 3
Two singleton sets are equal precisely when their only elements are equal. Therefore, from {2a + 1} = {7}, we obtain the equation 2a + 1 = 7. Subtracting 1 from both sides gives 2a = 6, and dividing by 2 gives a = 3. Substitution verifies the result: 2(3) + 1 = 7, so both singleton sets become {7}. Thus option B is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Two singleton sets are equal precisely when their only elements are equal. Therefore, from {2a + 1} = {7}, we obtain the equation 2a + 1 = 7. Subtracting 1 from both sides gives 2a = 6, and dividing by 2 gives a = 3. Substitution verifies the result: 2(3) + 1 = 7, so both singleton sets become {7}. Thus option B is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
