Discrete Mathematics Answers

Determine whether the statement p→(q∨r) is equivalent to (p∧∼r)→q ?

Let X= {1, 2, 3, 4}Y= {a, b, c} and Z={1,2}
1. Define K: Y→X as follows: K(a) = 1, K(b) = 2, K(c) = 3, and K(c) = 4. Is K onto? If not explain.
2. Using arrow diagram, find one function from X to Y that is Onto but not One-to-One
3. Define a function G: Y→Z that is onto and one-to-one and represent through matrix

If p→q is false can you find the truth value of ~ (p ∧ q) →q? Explain your answer.

Let X= {1, 2, 3, 4}Y= {a, b, c} and Z={1,2}
1. Define K: Y→X as follows: K(a) = 1, K(b) = 2, K(c) = 3, and K(c) = 4. Is K onto? If not explain.
2. Using arrow diagram, find one function from X to Y that is Onto but not One-to-One
3. Define a function G: Y→Z that is onto and one-to-one and represent through matrix.

Part (a): Let A and B are any sets then show that A-(A∩B)=(A∩A^c)∪(A∩B^c) by using membership table.
Part (b): Draw Venn diagram to describe sets A, B, and C that satisfy the given conditions.

A∩B≠ϕ,B∩C≠ϕ,A∩C=ϕ,A⊈B,C⊈B.

: Let A = {1, 2, 3, 4, 5} then define a relation R on A as (a.b)∈R iff a≤b and Relation Ton A as (a,b)∈T iff a/b.

Represent R by an matrix.
Is R Reflexive? Transitive? Give a valid reason for your answer.
Is T Antisymmetric? Give a valid reason for your answer.
Represent T by an matrix
Represent T by an arrow diagram.

Let X= {1, 2, 3, 4}Y= {a, b, c} and Z={1,2}
1. Define K: Y→X as follows: K(a) = 1, K(b) = 2, K(c) = 3, and K(c) = 4. Is K onto? If not explain.
2. Using arrow diagram, find one function from X to Y that is Onto but not One-to-One
3. Define a function G: Y→Z that is onto and one-to-one and represent through matrix.

Let A= {1, 2, 3, 4, 5}then define a relation R on A as (a.b)∈R iff a≤b and Relation Ton A as (a,b)∈T iff a/b.

Represent R by a matrix.
Is R Reflexive? Transitive? Give a valid reason for your answer.
Is T Antisymmetric? Give a valid reason for your answer.
Represent T by an matrix
Represent T by an arrow diagram.

Part (a): Let Aand B are any sets then show that A-(A∩B)=(A∩A^c)∪(A∩B^c) by using membership table.
Part (b): Draw Venn diagram to describe sets A, B, and C that satisfy the given conditions.

A∩B≠ϕ,B∩C≠ϕ,A∩C=ϕ,A⊈B,C⊈B.
Part (c): Find negation of the following statement: If cows are crows then crows are four legged.

Part (a): Determine whether the statement p→(q∨r) is equivalent to (p∧∼r)→q ?

Part (b): A survey team in Food Street is surveying of liking and disliking of people there. The food items to be considered in survey are of three types, Traditional heavy meals, Fast food, Dairy Products.

Draw Venn diagram and shade the areas separately which represent the following information
1.Traditional and Fast food liker but not Dairy product
2.Fast food or Dairy but not traditional
3.Dairy products and Traditional.