Discrete Mathematics Answers

Draw the digraph and the matrix of the relation R= {(1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3,4), (4, 1), (4, 2), (4, 3)} on the set A= {1, 2, 3, 4, 5}. Also decide whether it is reflexive,

whether it is symmetric, whether it is anti symmetric,whether it is transitive.

Consider the relation 𝑃 = {(1,7), (−1,7), (3,9), (1,3)}. Is 𝑃 a function? Justify your answer.

Use a Venn Diagram and shadings to find what X will be in terms of sets A en B and set operations so that :

A or B = (A/B) or (A and B) or X

With X disjoint To both A/B - A and B

Construct a formal proof of validity for the following argument. [10]

1. (N v O) → P

2. (P v Q) → R

3. Q v N

4. ¬ Q

∴ R

For propositions p, q, and r, determine whether 𝑝 ⟶ (𝑞 ⟶ 𝑟) and (𝑝 ⟶ 𝑞) ⟶ 𝑟 are logically equivalent.

If R, S and T are relations over the set A, then: Prove that (S∩T)∘R= (S∘R)∩(T∘R).

Let R be a relation from the set A to the set B, then: Prove that Ran (R)=Dom (R-1 ). 

 Let R be a relation over set A, then: Prove that IA∘R=R=R∘IA. 

We want to grade students by using IF or Nested if statement. The student name and marks are given. Write an IF or Nested IF statement to arrive at their grades i the grade column. The marks and the grades are as follows:

Less than 65 marks = c grade

More than or equal to 65 marks and less than 80 = B grade

More than or equal to 80 marks and less than 90 = A grade

More than or equal to 90 marks = A + grade

A B C

1. Student name Marks Grade
2. Shruti 42
3. Rakesh 97
4. Meena 66
5. Rahul 83

 If R, S and T are relations over the set A, then: Prove that If R⊆S, then T∘R ⊆ T∘S and R∘T ⊆ S∘T