Discrete Final Review

Front

What is a subset?

Back

A subset is a set that contains some or all elements of another set. For example, if A = {car, airplane, train}, then {car, train} is a subset of A.

Front

What does it mean for two graphs to be isomorphic?

Back

Two graphs are isomorphic if there is a one-to-one correspondence between their vertices and edges, meaning they have the same structure.

Front

How do you calculate the total number of combinations for making a sandwich with given choices?

Back

Multiply the number of choices for each category. For example, with 3 breads, 2 meats, and 2 toppings: 3 x 2 x 2 = 12 ways.

Front

What is a linear combination of vectors?

Back

A linear combination of vectors involves multiplying each vector by a scalar and adding the results. For example, 2i + 3j is a linear combination of unit vectors i and j.

Front

What is prime factorization?

Back

Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 105 is 7 x 5 x 3.

Front

Define a unit vector.

Back

A unit vector is a vector with a magnitude of 1, often used to indicate direction.

Front

What is the difference between a set and a subset?

Back

A set is a collection of distinct objects, while a subset is a set that contains elements from another set.

Front

Explain the concept of combinations in mathematics.

Back

Combinations refer to the selection of items from a larger set where the order does not matter.

Front

What is the formula for finding the number of combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to choose.

Front

What is a factor tree?

Back

A factor tree is a diagram used to break down a number into its prime factors.