# Mathematics Questions and Answers – Mathematical Reasoning – New Statements from Old

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Mathematical Reasoning – New Statements from Old”.

1. The denial of statement is called _____________
a) negation
c) contrapositive
d) compound

Explanation: The denial of statement is known as negation of the statement. It is denoted by ~p if statement is denoted by p.

2. The negation of a statement is also a statement.
a) True
b) False

Explanation: Yes, the negation of statement is also a statement. If the statement is true, its negation is false or if statement is false, its negation is true.

3. Which of the following cannot be the negation of the statement “Delhi is in India”?
a) Delhi is not in India
b) It is false that Delhi is in India
c) It is false that Delhi is not in India
d) It is not the case that Delhi is in India

Explanation: “Delhi is not in India”, “It is false that Delhi is in India”, “It is not the case that Delhi is in India” are negations of the given statement. Negation of a statement can be formed by adding ‘it is false that’ or ‘it is not the case that’. In statement “It is false that Delhi is not in India” two negation phrases are used which is wrong so it is not the negation statement.
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4. Which of the following cannot be the negation of the statement “Everyone in India speaks Hindi”?
a) Not everyone in India speaks Hindi
b) No person in India speaks Hindi
c) Someone in India does not speaks Hindi
d) At least one person in India who does not speaks Hindi

Explanation: Negation of everyone is not everyone. So, negation of the given statement should be “Not everyone in India speaks Hindi”, “Someone in India does not speaks Hindi”, “At least one person in India who does not speaks Hindi”. “No person in India speaks Hindi” cannot be the negation of the given statement as this means no one speaks Hindi which does not means not everyone.

5. Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?
a) There is at least one angle different in equilateral triangle
b) It is false that all angles are equal in equilateral triangle
c) It is not the case that all angles are equal in equilateral triangle
d) All angles are unequal in equilateral triangle

Explanation: Negation of all angles is ‘not all angles’. So, negation of the given statement is “There is at least one angle different in equilateral triangle”, “It is false that all angles are equal in equilateral triangle”, “It is not the case that all angles are equal in equilateral triangle”. But “All angles are unequal in equilateral triangle” cannot be the negation of given statement as this does not include isosceles triangles.

6. Which of the following is not negation of statement “Sum of 2 and 3 is greater than 4”?
a) Sum of 2 and 3 is smaller than 4
b) Sum of 2 and 3 is smaller than or equal to 4
c) Sum of 2 and 3 is not greater than 4
d) It is false that sum of 2 and 3 is greater than 4

Explanation: Negation of greater is ‘not greater’. ‘Not greater’ means either smaller than or equal to. So, “Sum of 2 and 3 is smaller than or equal to 4”, “Sum of 2 and 3 is not greater than 4”, “Sum of 2 and 3 is not greater than 4” are negation of the given statement. And “Sum of 2 and 3 is smaller than 4” is not the negation of given statement as it should include equal to also.

7. _____________ statement is made up of two or more statements where each statement is known as ________________ statement.
a) Compound, compound
b) Compound, component
c) Component, compound
d) Component, component

Explanation: A compound statement is made up of two or more statements where each statement is known as component statement.

8. Connect “0 is positive number” and “0 is a negative number”?
a) 0 is a positive or negative number
b) 0 is a positive and negative number
c) 0 is either positive or negative number
d) 0 is neither positive nor negative number

Explanation: “0 is a positive or negative number” is formed by connecting the given statements using or.

9. A rectangle is a quadrilateral and its four sides are equal. Which is not correct?
a) A rectangle is a quadrilateral is false
b) A rectangle has four sides is true
c) A rectangle is a quadrilateral is true
d) A rectangle has all sided equal is false

Explanation: A rectangle has four sides so it is a quadrilateral. All the four sides are not equal as two are equal and other two are equal.

10. Which of the following compound statement has both true component statements?
a) A prime number is divisible by 2 and odd
b) Two and two makes four or five
c) All integers are positive and divisible by 2
d) 100 is divisible by 2 and 5

Explanation: Prime number is not divisible by 2 always. Two and two makes our not five. All integers are not positive. 100 is divisible by 2 and 5 both. So, component statements of “100 is divisible by 2 and 5” are true.

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