How many elements are in A = {x : x is a letter in the word MATH}?
Answer and explanation
Correct answer: 4
A set contains distinct objects, and its cardinality is the number of distinct elements. The letters appearing in MATH are M, A, T, and H. Since all four letters are different, A = {M, A, T, H} and n(A) = 4. Thus the set is finite and option B is correct. Option A undercounts the letters, option C overcounts them, and option D incorrectly treats this word-based set as infinite.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A set contains distinct objects, and its cardinality is the number of distinct elements. The letters appearing in MATH are M, A, T, and H. Since all four letters are different, A = {M, A, T, H} and n(A) = 4. Thus the set is finite and option B is correct. Option A undercounts the letters, option C overcounts them, and option D incorrectly treats this word-based set as infinite.
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.
