Class 9 Propositions and their Converses Mock Test (CBSE)

Topics in Propositions and their Converses

• Propositions
• Converse of a proposition
• Counterexamples
• Proposition and converse both true
• Converse of the Baudhayana-Pythagoras theorem
• Other ways of writing 'if X then Y'

Propositions and their Converses practice questions with answers

1. Q1Multiple choice·1 mark
   Consider the proposition: 'If a quadrilateral is a square, then all its four sides are equal.' Which of the following represents the converse of this proposition?

   1. (a)If a quadrilateral has four equal sides and four right angles, then it is a square.
   2. (b)If a quadrilateral is not a square, then its four sides are not equal.
   3. (c)If all the four sides of a quadrilateral are equal, then it is a square.
   4. (d)If a quadrilateral does not have four equal sides, then it is not a square.
   Show answer and step marks

   1. Correct option: (c) If all the four sides of a quadrilateral are equal, then it is a square. The converse of an implication 'If P, then Q' is formed by interchanging the hypothesis and the conclusion to get 'If Q, then P'. Swapping the given parts yields 'If all the four sides of a quadrilateral are equal, then it is a square'.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   Which of the following sentences is a mathematical proposition?

   1. (a)Mathematics is interesting.
   2. (b)What is your name?
   3. (c)Please close the door.
   4. (d)The sum of the angles of a triangle is $180^\circ$.
   Show answer and step marks

   1. Correct option: (d) The sum of the angles of a triangle is $180^\circ$. A mathematical proposition is a declarative sentence that is definitively either true or false, but not both. Option (d) is a declarative statement with a definite truth value, whereas the others are a command, a question, and an opinion respectively.+1

   Answer: (d)
3. Q3Short answer·2 marks
   Consider the conditional statement: 'If a quadrilateral has all four sides equal in length, then it is a square.' State whether the statement is true or false. If it is false, give a counterexample.
   Show answer and step marks

   1. State that the given statement is false.+1
   2. Counterexample: a rhombus that is not a square, e.g. one with angles $60^\circ$ and $120^\circ$, has all four sides equal but its angles are not $90^\circ$.+1

   Answer: False. A rhombus that is not a square (e.g. with angles $60^\circ$ and $120^\circ$) has four equal sides but is not a square.

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