Mathematical Reasoning: Critical skills

This set of MCQs is based on the concepts and learning on mathematical reasoning, and its principle which is a part of mathematics where we determine the truth values of the given statements.

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The negation of a statement is also a statement.

True False

Which of the following cannot be the negation of the statement “Everyone in India speaks Hindi”?

Not everyone in India speaks Hindi No person in India speaks Hindi Someone in India does not speaks Hindi At least one person in India who does not speaks Hindi

Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?

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 All angles are unequal in equilateral triangle

Which of the following is a statement?

Roses are black. Mind your own business. Be punctual. Do not tell lies.

Which of the following is not a statement?

Smoking is injurious to health. 2 + 2 = 4 2 is the only even prime number. Come here.

The negation of the statement “7 is greater than 8” is

7 is equal to 8. 7 is not greater than 8. 8 is less than 7. none of these.

The contrapositive of the statement “If p, then q”, is

If q, then p. If p, then ~ q. If ~ q, then ~ p. If ~ p, then ~ q.

Which of the following is not a negation of the statement A natural number is greater than zero

A natural number is not greater than zero It is false that a natural number is greater than zero It is false that a natural number is not greater than zero None of these

The contra-positive of the statement If a triangle is not equilateral, it is not isosceles is

If a triangle is not equilateral, it is not isosceles If a triangle is equilateral, it is not isosceles If a triangle is not equilateral, it is isosceles If a triangle is equilateral, it is isosceles

If (p or q) is true, then

p is true and q is false p is true and q is true p is false and q is true All of the above

The denial of statement is called _____________.

Negation

Contradiction

Contrapositive

Compound

Which of the following cannot be the negation of the statement “Delhi is in India”?

Delhi is not in India

It is false that Delhi is in India

It is false that Delhi is not in India

It is not the case that Delhi is in India