Page 8 - LESSON NOTE

5. Write the contra positive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) It the two lines are parallel, then they do not intersect in the same plane.

Answer:

(i) The contra positive is as follows:

If a number x is not odd, then x is not a prime number.

The converse is as follows:

If a number x is odd, then it is a prime number.

(ii) The contra positive is as follows:

If two lines intersect in the same plane, then they are not parallel.

The converse is as follows:

If two lines do not intersect in the same plane, then they are parallel.

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6. Show that the statement “For any real numbers a and b, a = b implies that a = b” is not
true by giving a counter-example.
Answer:

The given statement can be written in the form of “if-then” as follows.

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If a and b are real numbers such that a = b , then a = b.
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Let p: a and b are real numbers such that a = b
q: a = b
The given statement has to be proved false. For this purpose, it has to be proved that if p,

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then ∼q. To show this, two real numbers, a and b, with a = b are required such that a ≠ b.
Let a = 1 and b = –1
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=> a = (1) = 1
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and b = (– 1) = 1
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So, a = b
However, a ≠ b
Thus, it can be concluded that the given statement is false.