I have a question, could you please help me out? For (1) & (2), Express in logic

Question

I have a question, could you please help me out?

For (1) & (2), Express in logical notation (quantifiers and connectives); For (3) & (4), State the converse; For (5), Translate into standard mathematical English (A really good answer uses no letters for variables and is brief).

(1). n is an even number.

(2). For every number that is a perfect cube, there is a larger number that is even.

(3). If lines l and m are parallel, then a transversal t to lines l and m cuts out congruent alternate interior angles.

(4). If the sum of the degree measures of the interior angles on one side of transversal t is less than 180 degree, then lines l and m meet on that side of transversal t.

(5).

Explanation / Answer

Answer of question (1)

Given statement is :

" n is an even number."

Now "There exists", "For all", are quantifires and "AND","OR" are connectives.

So using suitable quantifire and connective, given statement can be written as :

"There exists a number n and it is even."

This is the answer of question (1)

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