4.2 Quantifiers ‘All’ and ‘Some’ (Sample Questions)

Complete each of the following statements using the quantifiers ‘all’ or ‘some’ to make the statement true.

(a) _____ rectangles are squares.

(b) _____ prime numbers are odd numbers.

(c) _____ triangles have equal sides.

(d) _____ even numbers are divisible by 2.

(a) Some rectangles are squares.

(b) Some prime numbers are odd numbers.

(c) Some triangles have equal sides.

(d) All even numbers are divisible by 2.

Construct a true statement using the quantifier ‘all’ or ‘some’ for the given object and property.

(a) Object: multiples of 4

 Property: can be divided exactly by 5

(b) Object: regular hexagon

 Property: 6 equal sides

(c) Object: acute angles

 Property: less than 90^o

(a) Some multiples of 4 can be divided exactly by 5.

(b) All regular hexagons have 6 equal sides.

(c) All acute angles are less than 90^o.