Discrete Mathematics Answers

Suppose there are signs on the doors to two rooms. The sign on the first door reads “In this

room there is a lady, and in the other one there is a tiger”; and the sign on the second door

reads “In one of these rooms, there is a lady and in one of them there is a tiger.” Suppose

that you know that one these signs is true, and the other is false. Behind which door is the

lady? Explain your reasoning using propositions.

A compound proposition is satisfiable if there is an assignment of truth values to its

variables that makes it true (that is when it is a tautology or a contingency)

Determine whether the compound proposition is satisfiable:

(p → q) ∧ (p → ¬q) ∧ (¬p → q) ∧ (¬p → ¬q)

Construct a truth table for each of these compound propositions

(p → q) ⊕ (¬p ↔ ¬r)

How many strings begin with the letter F and do not end with EB ?

Draw flow charts to this questions.

Exercise 1.

1. Input two numbers to find the highest number and then display it.

Exercise 2.

1. Modify the Exercise 1 to find the both highest and the lowest to display them.

Exercise 3.

1. Input the session code and display the appropriate season as follows:

• Season code-Season-1-Autumn
• 2-Winter
• 3-Spring
• 4-Summer

Directions: Read each statement carefully, show your complete solution if needed.

1. Write the Converse, Inverse, and Contrapositive of: "If 25 is an integer, then 25 is a rational number."

2. Use De Morgan's laws to write the given statements in their equivalent form: "Either I will not vote for you or I will not campaign for you"

3. Use a truth table to show that p ‹—› q = [(p —› q) ^ (q —› p)].

4. Write the argument in symbolic form (row form), use a truth table to determine if the argument is valid or invalid.

5. Use Euler diagram to determine whether the argument is valid or invalid. "All square are not triangles. Some triangles are equilateral. All squares are not equilateral."