If A = {x ∈ Z : x leaves remainder 5 when divided by 4}, what is A?
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Answer and explanation
Correct answer: A = ∅
In Euclidean division by 4, the remainder must be one of 0, 1, 2, or 3; it must always be less than the divisor. Therefore, no integer can leave remainder 5 when divided by 4. The defining condition has no solution, so A has no elements and is the empty set. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
In Euclidean division by 4, the remainder must be one of 0, 1, 2, or 3; it must always be less than the divisor. Therefore, no integer can leave remainder 5 when divided by 4. The defining condition has no solution, so A has no elements and is the empty set. Hence, option A is correct.
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.
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