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Suppose ℤ denotes the set of all integers, ℤ+ denotes the set of all positive integers, and ℤ− denotes the set of all negative integers. Similarly ℝ denotes the set of all real numbers, ℝ+ denotes the set of all positive real numbers, and ℝ− denotes the set of all negative real numbers. Suppose ℕ denotes the set of all natural numbers and ℚ denotes the set of all rational numbers. Enter "T" for each true, and "F" for each false statements.(a) Z / Q = Z(b) Z / Z- = Z+

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Answer:

a) False

b) False          

Step-by-step explanation:

We are given the following information in the question:

[tex]Z[/tex] denotes the set of all integers.

[tex]Z^+[/tex] denotes the set of all positive integers.

[tex]Z^-[/tex] denotes the set of all negative integers.

[tex]Q[/tex] denotes the set of all rational numbers

a) False

We will give a counter example .

[tex]\displaystyle\frac{Z}{Q}\\\\\displaystyle\frac{3}{\frac{2}{3}} = \displaystyle\frac{9}{2} \notin Z[/tex]

b) False

We will give a counter example .

[tex]\displaystyle\frac{Z}{Z^-}\\\\\displaystyle\frac{3}{-3} = -1 \notin Z^+[/tex]

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