a and b are two rational numbers such that a + b = 3. When we divide a by b, the closure property of rational numbers does not hold true. The values of ab and a - b respectively are:
0, -3
0, 0
0, 3
3, 3
Rational Numbers
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Question

a and b are two rational numbers such that a + b = 3. When we divide a by b, the closure property of rational numbers does not hold true. The values of ab and a - b respectively are:
0, -3
0, 0
0, 3
3, 3

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KnowledgeBoat · Accepted Answer

Rational numbers are closed under division only when the divisor is a non-zero rational number, as division by 0 is not defined.

As a ÷ b does not satisfy the closure property, the divisor b must be 0.

⇒ b = 0

⇒ a + b = 3

⇒ a + 0 = 3

⇒ a = 3

Finding the values of ab and a - b,

⇒ ab = 3 × 0 = 0

⇒ a - b = 3 - 0 = 3

Hence, Option 3 is the correct option.