If R={x:x∈N, x+4=4}, what is R?
Answer and explanation
Correct answer: R=∅
The governing concept is that a set-builder condition must be solved within its stated domain. Solving x+4=4 gives x=0. With the convention specified here, N={1,2,3,...}, so 0 is not a natural number. Therefore the equation has no solution in N, even though it has the solution 0 in the whole-number domain. The set contains no elements and is therefore ∅, so C is correct.
Frequently asked questions
What is the correct answer to this question?
R=∅
Why is this the correct answer?
The governing concept is that a set-builder condition must be solved within its stated domain. Solving x+4=4 gives x=0. With the convention specified here, N={1,2,3,...}, so 0 is not a natural number. Therefore the equation has no solution in N, even though it has the solution 0 in the whole-number domain. The set contains no elements and is therefore ∅, so C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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