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ser-zykov [4K]
3 years ago
8

Translating mathematical statements in English into logical expressions. info About Consider the following statements in English

. Write a logical expression with the same meaning. The domain is the set of all real numbers. (a) There is a number whose cube is equal to 2. (b) The square of every number is at least 0. (c) There is a number that is equal to its square. (d) Every number is less than or equal to its square.
Mathematics
1 answer:
arsen [322]3 years ago
3 0

Answer:

See below

Step-by-step explanation:

(a) There is a number whose cube is equal to 2.

\large \exists x \in \mathbb{R}\;|\;x^3=2

(b) The square of every number is at least 0.

\large \forall x\in \mathbb{R},\;x^2\geq 0

(c) There is a number that is equal to its square.

\large \exists x \in \mathbb{R}\;|\;x^2=x

(d) Every number is less than or equal to its square.

\large \forall x\in \mathbb{R},\;x\leq x^2

(By the way, this last statement <u>is not true</u> when 0 < x < 1)

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