Basic Mathematics

Refer the following table, where in the first column four pairs of two vectors are shown and in the second column some possible outcomes of basic mathematical operation on these vectors are given. Suggest suitable match(s).

In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach. Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teaches teaching only Mathematics is:

There are 11 teachers who teach Mathematics or Physics in a school, Of these, 7 teach Mathematics and 3 teach both Mathematics and Physics. How many teach Physics?

Basics of Mathematical Reasoning | Truth Tables and Laws