Is phyhsics,philosophy of mathematical sceince?

Use principle of mathematical induction to prove that: 1+2+3+……….+n=(n(n+1))/2

Use the principle of mathematical induction to show that a^(n) - b^n) is divisble by a-b for all natural numbers n.

A class has 175 students. The following is the description showing the number of students studying one or more of following subjects in this class. Mathematics 100 , Physics 70, Chemistry 46, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18 : Find : the number of students who are enrolled in Mathematics alone, Physics alone and Chemistry alone .

Prove the rule of exponents , (ab)^n= a^n b^n by using Principle of Mathematical Induction for every natural number.

By Principle of Mathematical Induction, prove that : 2^n >n for all n in N.

What is resistance ? Also, discuss mathematical relation. Write its units.

In a college 30% students fall in physics 25% fall in mathematics and 10% fall in both one student is chosen at random, the probability that the student falls in Physics if he she has fallled in mathematics is

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had takes Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all three subjects. Find the number of students that had taken : Physics and Chemistry but not Mathematics.

In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach Physics and Mathematics. How many teach Physics?