a) There does not exist an integer b such that for a>1, a×b=b×a=b

b) The product of a positive and a negative integer is positive.

c) Subtraction follows commutative property.

d) All are false.

# Which of the following statements is true?

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Let’s analyze each statement one by one and determine their truth values:

a) There does not exist an integer b such that for a>1, a×b=b×a=b.To prove this statement true, we need to show that there is no integer b that satisfies the given conditions. Let’s consider an arbitrary integer a > 1. For any value of b, we have:

a × b = a × 1 = a ≠ b

Thus, there is no integer b that satisfies the equation a × b = b × a = b. Therefore, statement a is true.

b) The product of a positive and a negative integer is positive.

This statement is false. The product of a positive integer and a negative integer is always negative. For example, if we consider 3 as a positive integer and -2 as a negative integer, we have:

3 × (-2) = -6

Since the product is -6, which is negative, the statement is false.

c) Subtraction follows the commutative property.

This statement is false. The commutative property of subtraction does not hold. For example:

5 – 3 = 2

3 – 5 = -2

Since 2 and -2 are not equal, subtraction does not follow the commutative property.

The correct answer is

a) There does not exist an integer b such that for a>1, a×b=b×a=b.