Understanding Functions: Total, Injective, and Increasing

The video tutorial explains how to map a function from one set to another, focusing on calculating the total number of functions, injective functions, and increasing functions. It uses the counting principle and permutations to determine injective functions and combinations for increasing functions. The tutorial provides a step-by-step breakdown of these concepts using two-line notation and mathematical formulas.

What is the function f mapping in this tutorial?

• From set {1, 2, 3} to set {1, 2, 3}

• From set {1, 2, 3} to set {1, 2, 3, 4, 5, 6}

• From set {1, 2, 3, 4, 5, 6} to set {1, 2, 3, 4, 5, 6}

• From set {1, 2, 3, 4, 5, 6} to set {1, 2, 3}

How many total functions can be formed from the given sets?

• 216

• 72

• 432

• 36

What principle is used to calculate the total number of functions?

• Additive principle

• Multiplicative principle

• Subtractive principle

• Divisive principle

What defines an injective function?

• Every element of the domain maps to multiple elements of the co-domain

• Every element of the co-domain is the image of at most one element from the domain

• Every element of the domain maps to itself

• Every element of the co-domain maps to multiple elements of the domain

How many injective functions are possible from the given sets?

• 90

• 150

• 120

• 60

Which mathematical concept is used to calculate the number of injective functions?

• Integration

• Combination

• Differentiation

• Permutation

What is the condition for a function to be increasing?

• If a is less than b, then F of a is greater than F of b

• If a is greater than b, then F of a is less than F of b

• If a is greater than b, then F of a is greater than F of b

• If a is less than b, then F of a is less than F of b

How many increasing functions can be formed from the given sets?

• 10

• 15

• 20

• 25

What method is used to determine the number of increasing functions?

• Division

• Permutation

• Subtraction

• Combination

What is the result of 6 choose 3 in the context of increasing functions?

• 25

• 20

• 15

• 10