Question

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.

Answer 1

See below

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 is not true when 0 < x < 1)