Discrete Mathematics Answers

let ′ ∣ ′ be the divides relation on a set of positive integers. That

is ∀𝑎, 𝑏 ∈ 𝐴, 𝑎 ∣ 𝑏 ⇔ 𝑏 = 𝑘. 𝑎 for some integer 𝑘. Prove that ∣ is a partial order

Relation.

Let R be a reflexive relation on a set A. Show that R ⊆ R².

Create the logic circuit diagram for z F= X’Y + XZ

Given F(w, x, y, ) = w'x'y'z' + w'x'y'z + w'xyz' + w'xyz, express F’(w,x,y,z) in minterm list form. Draw its corresponding truth table.

Find the sum-of-products expansions of these Boolean functions. F(A, B,C) = C 

Determine weather the each of the following function from set (a,b c, d)to itself injective

1- the function sending the order quadruple (a,b,c,d)to (b,a,c,d)

2- the function sending the order quadruple (a,b,c,d)to (b,b,d,c)

3- The function sending the order quadruple (a,b,c,d) to ( b,d,c,d)

Let R be a reflexive relation on a set A. Show that R ⊆ R².