4_MATH2572___DISCRETE_MATHEMATICAL_STRUCTURES_Sessional__I (1)

What are the sets A and B if A−B={1,5,7,8}, B−A={2,10}, and A∩B={3,6,9}?

A contains elements not in B, while B contains elements not in A.

How many students must be in a class to guarantee at least two students receive the same score from 0 to 30?

At least 31 students are needed due to the pigeonhole principle.

What does (A∪B)̅ equal in terms of A and B?

It equals A̅ ∩ B̅, showing the complement of the union.

What is g∘f if f(x)=3x−2 and g(x)=2x+1?

g∘f results in a new function combining both definitions.

Are the functions g∘f and f∘g onto?

Determining onto requires checking if every possible output is achieved.

How many ways can a committee of 4 from mathematics and 6 from computer science be selected?

Use combinations to calculate the total selections from each department.

What are the coefficients of x^8y^9 and x^9y^8 in the expansion of (3x−2y)^17?

These coefficients can be found using the binomial theorem.

What is the equivalence relation defined by xRy if x−y is divisible by 5?

It satisfies reflexivity, symmetry, and transitivity.

Is the relation R defined by xRy if x divides y a partial order?

It is a partial order but not symmetric.

How do you prove that 3^(n+1) + 4^(2n−1) is divisible by 13 using induction?

Base case and inductive step must show divisibility holds for all n.

What is the solution to the recurrence relation an = −3an−1 − 3an−2 − an−3?

Initial conditions guide the specific solution for n≥3.

What are the sets A and B if A−B={1,5,7,8}, B−A={2,10}, and A∩B={3,6,9}?

A contains elements not in B, while B contains elements not in A.

How many students must be in a class to guarantee at least two students receive the same score on a scale from 0 to 30?

At least 31 students are needed due to the pigeonhole principle.

What does (A∪B)̅ equal in terms of A and B?

It equals A̅ ∩ B̅, showing the complement of the union.

What is g∘f if f(x)=3x−2 and g(x)=2x+1?

g∘f results in a new function combining both definitions.

Are the functions g∘f and f∘g onto?

Determining onto requires checking if every output is achieved.

How many ways can a committee of 4 from mathematics and 6 from computer science be selected?

Use combinations to calculate the total selections.

What are the coefficients of x^8y^9 and x^9y^8 in the expansion of (3x−2y)^17?

These coefficients can be found using the binomial theorem.

What is the equivalence relation defined by xRy if x−y is divisible by 5?

It satisfies reflexivity, symmetry, and transitivity.

Is the relation R defined by xRy if x divides y a partial order?

It is a partial order but not symmetric.

How do you prove that 3^(n+1) + 4^(2n−1) is divisible by 13 for every positive integer n?

Use mathematical induction to establish the divisibility.

What is the solution to the recurrence relation an = −3an−1 − 3an−2 − an−3 for n≥3?

Initial conditions are needed to find specific terms.