Discrete Mathematics Answers

Let R={(1,3),(4,2),(2,4),(2,3),(3,1) } be a relation on the A={1,2,3,4}. Find the transitive closure of R using Warshall’s algorithm.

For real number x and y, we write xRy⇔x-y+√2 is an irrational number. Is the relation
(a) Equivalence
(b) Partial order

Let R be the relation from A={2,3,4,5} to B={3,6,7,10} defined by ‘x divides y’,
(a) thenR^(-1) is equal to:
(b) Is R an equivalence relation?

Determine the following relation is an equivalence relation or not. If the relation is an equivalence relation, describe the partition given by it. xRy if x>yx,y∈the set of all real numbers

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.