Discrete Mathematics Problem. Please give me just answer no need explanation. Just right answer. Answer like 1. a 2. b like that.

Question 1: Consider a binary relation R for all integers x and y:

xRy iff (x+y) is a multiple of 4.

Which of the following is TRUE?

a)We don't have sufficient information to determine this.

b) R is reflexive, i.e. xRx for any x.

c) R is neither reflexive nor anti-reflexive.

d) R is anti-reflexive, i.e. xRx for no x.

Question 2: The following relations are defined for all integers x and y.

Which one of the is transitive?

a) xRy iff xy is even

b) xRy iff (x-y) is odd.

c) None of the three.

d) xRy iff (x-y) is even.

Question 3: Consider the following relations defined for all real numbers x and y.

Which relation is symmetric?

a) xRy iff x+2y=3.

b) xRy iff x-y=1.

c) xRy iff x+y=2.

d) None of the three.

Question 4: Which of the following is FALSE based on the directed graph G?

a) G is anti-reflexive because none of these relations are self-relating loops.

b) For the point 11, (in-degree)=2 and (out-degree)=3.

c) G is anti-symmetric because none of these relations are in both directions.

d) None of the three.

Question 5: Consider the relation G given by the graph:

Which of the following is FALSE?

a) There is a cycle that passes all 4 points.

b) None of the three.

c) There is a circuit that passes all 4 points.

d) 1G³1

Question 6: Consider the partial order described by the following Hasse diagram:

Which of the following is FALSE?

a) 1010 ?1011

b) None of the three.

c) 1001?0111

d) 0000?x for any point x.

5 10 3