Binary operations, sets and the binomial theorem

Question 1 of 10

Which binary operation on the real numbers is commutative?

Question 2 of 10

If a * b = 2a − b, find (3 * 1) * 2.

Question 3 of 10

A binary operation is defined by a * b = a + b − ab. Find 2 * 3.

Question 4 of 10

A binary operation is defined by a * b = ab/(a + b) for positive reals. Is * commutative?

Question 5 of 10

How many subsets does a set with 4 elements have?

Question 6 of 10

Find the coefficient of x² in the expansion of (1 + 2x)⁴.

Question 7 of 10

The number of terms in the expansion of (a + b)⁶ is

Question 8 of 10

n(A) = 20, n(B) = 15 and n(A ∩ B) = 8. Find n(A ∪ B).

Question 9 of 10

A binary operation * is defined by a * b = a + b + ab. Find 2 * 3.

Question 10 of 10

If x ⊕ y = x + y − 2, find the identity element.