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

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 is not true when 0 < x < 1)