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Let a relation T on the set R of real numbers be T = {(a,b) : 1 + ab < 0, a,∈ R}. Then from among the ordered pairs (1,1) (1,2)(1,-2)(2,2), the only pair that belongs to T is________.​
  • a)
    (2,2),
  • b)
    (1,1),
  • c)
    (1,-2)
  • d)
    (1,2)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let a relation T on the set R of real numbers be T = {(a,b) : 1 + ab &...
Relation T on R of real numbers

Definition of Relation T: T is a relation on the set R of real numbers and it is defined as T = {(a,b) : 1 ≤ ab ≤ 0, a ε R}

Explanation: This means that T is a set of ordered pairs (a,b) such that a is a real number and b is a real number, and the product of a and b is between 1 and 0, inclusive. In other words, either a and b are both negative or one of them is negative and the other is between 0 and 1.

Given ordered pairs: (1,1), (1,2), (1,-2), (2,2)

Checking which pairs belong to T:

- (1,1): 1 ≤ 1*1 ≤ 0 is false, so (1,1) does not belong to T
- (1,2): 1 ≤ 1*2 ≤ 0 is false, so (1,2) does not belong to T
- (1,-2): 1 ≤ 1*(-2) ≤ 0 is true, so (1,-2) belongs to T
- (2,2): 1 ≤ 2*2 ≤ 0 is false, so (2,2) does not belong to T

Conclusion: The only ordered pair that belongs to T is (1,-2). Therefore, the correct answer is option C, (1,-2).
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Community Answer
Let a relation T on the set R of real numbers be T = {(a,b) : 1 + ab &...
Since T is a set of real number for it's given ordered pairs we have a condition provided that is 1 + ab is less than zero. so in the given option c if we put order of a and b then it satisfy our given condition
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Let a relation T on the set R of real numbers be T = {(a,b) : 1 + ab < 0, a,∈ R}. Then from among the ordered pairs (1,1) (1,2)(1,-2)(2,2), the only pair that belongs to T is________.​a)(2,2),b)(1,1),c)(1,-2)d)(1,2)Correct answer is option 'C'. Can you explain this answer?
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