Question

Let p: A number is greater than 25.

Let q: A number is less than 35.

If p ∧ q is true, then what could the number be? Check all that apply.

24
28
32
36
40

Answer 1

We are given that:
p is greater than 25, this means that p>25
p ∈ ]25,∞[ ...........> interval I

q is less than 35, this means that q<35
q ∈ ]-∞,35[ ...........> interval II

The given condition p ∧ q is true means that (p and q) is true. In other word, their intersection is true.
Therefore, the final result would be the intersection between the two intervals (interval I and interval II)

Bases on the above, the final answer would be:
]-∞,35[ ∧ ]25,∞[ which is ]25,35[

Answer 2

The correct options are:

28 , 32

Explanation:

We are given a conditional statement p as:

p: A number is greater than 25.

This is the collection of all the real numbers which are greater than 25.

i.e. the set p is given by:

p= (25,∞)

Similarly,

The conditional statement q is given by:

q: A number is less than 35.

This is the collection of all the real numbers which are less than 35.

i.e. the set q is given by:

p= (-∞,35)

Now we are asked to find:

p∧q which is the intersection if the elements of the two set.

Hence,

p∧q= (25,35)

is the collection of elements which are greater than 25 and less than 35.

1)

24

as we see that 24∉ (25,35)

Hence, option: 1 is incorrect.

2)

28

as we see that: 28∈ (25,35)

Hence, option: 2 is correct.

3)

32

Similarly 32 ∈ (25,35)

Hence, option: 3 is correct.

4)

36

Here 36 ∉ (25,35)

Hence, option: 4 is incorrect.

5)

40

Again 40 ∉ (25,35)

Hence, option: 5 is correct.