Q11 of 18 Page 13

Write the contra positive and converse of the following statements.

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

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

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4


(i) The contra positive statement for the statement "If x is a prime number, then x is odd" is "If a number is not odd, then x is not a prime number".

The converse statement for the statement "If x is a prime number, then x is odd" is "If a number x is odd, then it is a prime number".

(ii) The contra positive statement for the statement "If the two lines are parallel, then they do not intersect in the same plane" is "If two lines intersect in the same plane, then they are not parallel" and the converse statement is "If two lines do not intersect in the same plane, then they are parallel.

(iii) The contra positive statement for the statement "Something is cold implies that it has low temperature" is "If something is not at low temperature, then it is cold" and the converse statement is "If something is at low temperature, then it is cold.

(iv) The contra positive statement for the statement "You cannot comprehend geometry if you do not know how to reason deductively" is "If you know how to reason deductively, then you cannot comprehend geometry" and the converse statement is "If you do not know how to reason deductively, then you cannot comprehend geometry".

(v) The contra positive statement for the statement "x is an even number implies x is divisible by 4" is "If x is not divisible by 4, then x is not an even number" and the converse statement is "If x is divisible by 4, then x is an even number.

More from this chapter

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9
State whether the "OR" used in the following statements is "exclusive" or "inclusive". Give reasons for your answer.

(i) Sun rises or moon sets.

(ii) To apply for a driving license, you should have a ration card or a passport.

(iii) A lady gives birth to a baby boy or baby girl.

(iv) All integers are positive or negative.

10
Rewrite the following statement with "if-then" in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

12
Write each of the following statements in the form of "if-then"

(i) You get a job implies that your credentials are good.

(ii) The Banana tree will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.

13
Given statements in (a) and (b).
Identify the statements given below as contra positive or converse of each other.
(a)
(i) If you live in Delhi, then you have winter clothes.
(ii) If you do not have winter clothes, then you do not live in Delhi.

(b)
 (i) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(ii) If the diagonals of a quadrilateral do not bisect each other, then the
quadrilateral is not a parallelogram.