Determine the truth values of these statements
a) the product of x 2 and x 3 is x 6 .
b) 2π + 5π = 7π
c) x 2 > 0 for any real number.
d) the integer 315 − 8 is even.
e) the sum of two odd integers is even.
f) √ 2 ∈ z
g) −1 ∈/ z +
h) π ∈ q

a) False b) True c) False d ) False e) True f) False g) False h) False

Step-by-step explanation:

a) False

x² × x³ =

When we multiply two exponential number with same base, their powers add up.

b) True

2π + 5π = π(2+5) = 7π

The coefficients of π are added together.

c) False

x² ≥ 0. For any value of x, negative or positive x² is always positive. But for x = 0, x² = 0×0 = 0

d) False

315 - 8 = 307, which is clearly an odd number.

e)True

The sum of all integers is always even.

Let m and n be two odd integers.

Thus, they can be expressed as m = 2r + 1 and n = 2s +1, where r and s are even integers.

m + n = 2r +2s + 2, which is clearly even.

f) False

Since √2 is an irrational number. It cannot belong to z, which is collection of all integer number.

√2 ∉ z

g) False

Since -1 is a negative integer, it cannot belong to , as it is collection of all positive integers.

h) False

π cannot belong to Q because Q is a collection of all rational numbers and π is not a rational number. The decimal expansion of π is non- terminating that is it does not end.

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Step-by-step explanation: