∀x ∈ℝ, x<2 ⇒x2<4

Mj K

Mj K

Answered question


say if this statement is true or false with justification

x , x<2 x2<4

Answer & Explanation



Expert2023-04-25Added 533 answers

The statement in question is:
For all x, if x<2, then x2<4

To determine if this statement is true or false, we need to check if it holds for all real numbers x less than 2.

Let's begin by assuming that x is a real number less than 2. Then, we know that x is negative or positive and lies between negative infinity and 2.

We can square both sides of the inequality x<2 to obtain:

This is true for all real numbers x that are less than 2. Therefore, the statement is true.

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