How to explain the problem?

Question

Mathematics

Please explain how to solve these problems.
I know that predicate logic is applied here, but I don’t understand how it is applied in these tasks.

Answer 1

For the first task. Here you need to use your imagination and show ingenuity in order to compose the one you need from the available predicates.
Here you have 4 beams ab ac ad ae. the predicate means that the angles bac, cad and dae are equal.
But there is nothing about angles in these predicates. But angles can be proved through equal triangles. How to construct equal triangles on these rays? For example. one can plot the same length along all three rays, and then the third sides b'c', c'd' and d'e' must be equal.
Set aside the length ab, for example. Then the desired predicate is that there are points c' on the ray ac, d' on the ray ad, and e' on the ray ae such that ab'=b'c'=c'd'. All the conditions in this statement are expressed through the predicates given to you.
About the second task, well, rewrite it in a mathematical way. Expand the predicates, write equations and see if there is a solution. If there is a solution, then there are such y and z and the predicate is true.