Mathematical reasoning(form 4)- Worksheet quantifier.

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Worksheet 1 (Quantifier ‘all’ or ‘some’.)

1) Rewrite the following statements by using the quantifier ‘all’ or ‘some’ without
changing the meaning of the statement.

a. Several isosceles triangles are equilateral triangles.
b. Any perfect square is a square of a whole number.
c. Not many of the double digit whole numbers are prime numbers.
d. Every mixed number can be converted to an improper fraction.

2) Determine whether each of the following statements is true or false.

a. All integers can be written as a fraction.
b. Al right-angled triangles have the longest side opposite the right-angled
triangle.
c. All prime numbers do not have factors.
d. All sets produce an empty set when they intersect with an empty set.

3) State whether each statement below is true or false. Give an example to support
your answer.

a. All multiples of 12 are divisible by 4.
b. All cube roots of a negative number is a negative number.
c. All fractions can be written in the form p/q, where p and q are integers
and p is greater than q.
d. Al1 the subsets of the set {2, 3, 4, 5} contain at least on element.

4) Determine whether each of the following statements can be generalized by using
the quantifier ‘all’.

a. A negative integer q gives rise to a positive integer when it is squared.
b. The even number 8 is divisible by 4.
c. Trapezium ABCD has two parallel sides.
d. Pentagon PQRST has five sides.

5) Based on the object and the property given in each of the following, construct a
true statement using the quantifier ‘all’ or ‘some’.

a. Object : Integer.
Property : Whole number.

b. Object : Kites.
Property : One axis of symmetry.

c. Object : Fractions.
Property : Smaller than 1.

d. Object : Right angles.
Property : 900

e. Object : Rectangles.
Property : Equal opposite sides.