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Mathematical Reasoning

Short Answer Type

81. State the converse and contrapositive of the following statement.
p : A positive integer is prime only if it has no divisors other than 1 and itself.

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82. State the converse and contrapositive of the following statement.
q : I go to a beach whenever it is a sunny day.

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83. State the converse and contrapositive of the following statement.
r : If it is hot outside, then you feel thirsty.

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84. Rewrite the following statement in the form “p if and only if q”.
p : If you watch television, then your mind is free and if your mind is free, then you watch the television.

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85. Rewrite the following statement in the form “p if and only if q”.
q : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

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86. Rewrite the following statement in the form “p if and only if q”.
r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

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87. Write the following statement in five different ways, conveying same meaning.
p : If a triangle is equiangular, then it is an obtuse angled triangle.

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88.

Write the component statements of it and use them to check whether the compound statement is true or not.
t : You are wet when it rains or you are in a river.

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89.

Check the validity of the following statement.
“Square of an integer is positive or negative”.

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90.
Show that the statement “The integer n is even if and only if n² is even’ is true.

Solution not provided.

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Previous Year Papers

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Test Yourself

Short Answer Type

90. Show that the statement “The integer n is even if and only if n2 is even’ is true.

90.
Show that the statement “The integer n is even if and only if n² is even’ is true.