Discrete Mathematics Answers

•Construct the truth table of the converse,

contrapositive, and inverse of p→ q

•Let p, q, and r be propositions. Construct the

truth table of r→(˥p⋀q)

1.    Show that are logically equivalent. P ↔ Q and (P ∧ Q) V ( ¬P ∧ ¬Q)

 Your answer sheets showing your name and solution.

1. Given the following:

·        g: "You can graduate."

·        m: "You owe money to the college."

·        r: "You have completed the requirements of your major."

·        b: "You have an overdue book."

Translate "You can graduate only if you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book." into a propositional logic.

2. Show that  are logically equivalent.

3. Show, by the use of the truth table (truth matrix), that the  is a contradiction.

Given

[1 1 -1]

A=[2 2 3]

[4 0 0]

[1 1 -1]

b=[2 2 3]

[4 0 0]

1.Find –A^-1+ 3B^T

2.Find B^-1+ ( A^T+A^-1)

Solve for the determinant in the equation below

2 −2 1

2 2 1

4 1 3

  Find the product of 10101₂ and 101₂.  

1. Convert 172 to the following equivalences:

octal

hexadecimal

Show ALL working

1.  Convert the following to their decimal equivalence:

2022₈

ACE₁₆

1.  Convert the following to their binary equivalence:

635₈

FAB5₁₆

Convert the decimal fraction 55.231₁₀ to its binary equivalence.