Discrete Mathematics Answers

Let R be the relation {(1,1),(1,3),(2,2),(3,1),(3,2)}.

(a) Find the 3x3 matrix MR representing R.

(b) Find the matrix representing the transitive closure of R.

Consider the two relationsdefined on the set of all people. (i) (a,b)  R, iff a is taller than b (ii) (a,b)  R, iff a and b were born on the same day. Determine whether the relations are reflexive, symmetric, antisymmetric and/or transitive

Write the negation of the flowing statement :∃x∈R,x>3⇒x^2>9.

Let A={1,2,3,4,5}, determine the truth value of the following:

i.(∀x∈A)(x+3=10),ii.(∃x∈A)(x+3<5).

Write the following statement in symbolic form using quantifiers:

I. All students have taken a course in Mathematics

II. Some students are intelligent, but not hardworking.

Is the following argument valid?


If Taxes are lowered, then income rise.

Income rise.

Therefore Taxes are lowered.

Given the following statements as premises:

If he takes coffee, he does not drink milk.

He eats crackers only if he drinks milk.

He does not take soup unless he eats crackers.

At noon today, he had coffee.

Therefore he took soup at noon today.

Verify the validity of the statements.

Find the coefficient of x^18 in the expansion of (1-x-x^2)^10

Write down the converse of each of the following statements: (2)

i) If n =1 (mod 4) for a natural number n, then n = x^2+y^2 for two integers

x and y.

1. Discuss two examples on binary trees both quantitatively and qualitatively