# Discrete Mathematics Quiz By: Layth Adeeb

By Layth Slewa
Layth Slewa, Cyber Security
Layth, a passionate and professional technical consultant in Mobile Communications and Cyber Security, combines expertise to excel in these crucial fields.
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Welcome To Discrete Mathematics QuizDesigned By Layth AdeebCihan University / Faculty of Computer Science / First Semester

• 1.

### "Baghdad is the Capital of Iraq"  choose all that apply

• A.

It is a Statement

• B.

The Truth Value of the Proposition is True

• C.

The Truth Value of the Proposition is False

• D.

It is a proposition

A. It is a Statement
B. The Truth Value of the Proposition is True
D. It is a proposition
Explanation
The given answer is correct because it correctly identifies that the statement "Baghdad is the Capital of Iraq" is indeed a statement. It also correctly states that the truth value of the proposition is true, meaning that the statement is factually correct. Lastly, it correctly identifies that the statement is a proposition, which is a declarative sentence that can be either true or false.

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• 2.

• A.

It is a Statement

• B.

It is a Proposition

• C.

It's a Request (only Statements can be Propositions)

• D.

The Truth Value of the proposition is True

C. It's a Request (only Statements can be Propositions)
Explanation
The given answer states that "Please Charge my Phone" is a request and not a proposition. This is because propositions are statements that can be either true or false, whereas a request is not a statement that can be evaluated for truth value. Therefore, "Please Charge my Phone" cannot be a proposition and is instead classified as a request.

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• 3.

### "x<y if and only if y>x". why we consider this statement as a proposition?

• A.

Because the Value of x is greater than y

• B.

Because its Truth value does not depend of specific values of x and y

• C.

Because the Value of x is less than y

• D.

Because x and y are variables

B. Because its Truth value does not depend of specific values of x and y
Explanation
The statement "xx" is considered a proposition because its truth value does not depend on specific values of x and y. This means that regardless of what values x and y take, the statement will always be either true or false. The truth value of the statement is solely determined by the relationship between x and y, not their actual numerical values.

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• 4.

### "y>5"  This Statement is not a Proposition Because y is a ___________

Variable
unknown
not defined
changable
Explanation
The statement "y>5" is not a proposition because "y" is a variable. A proposition is a statement that is either true or false, but since "y" is not defined or given a specific value, it cannot be determined whether the statement is true or false. Therefore, it is not a proposition.

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• 5.

### A statement that is always true

• A.

Tautology

• B.

A. Tautology
Explanation
A tautology is a statement that is always true, regardless of the truth values of its individual components. This means that every possible combination of truth values for the components will result in the statement being true. In contrast, a contradiction is a statement that is always false. Therefore, the correct answer is "Tautology" because it accurately describes a statement that is always true.

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• 6.

### Which of the following formulas Belong to the Contradiction

• A.

Râˆ¨(Â¬r)

• B.

Râˆ§(Â¬r)

• C.

Â¬(Â¬(pâˆ§q)â†”(Â¬p)âˆ¨(Â¬q))

• D.

Â¬(pâˆ§q)â†”(Â¬p)âˆ¨(Â¬q)

B. Râˆ§(Â¬r)
Explanation
The formula râˆ§(Â¬r) belongs to the contradiction. This is because the formula represents the logical conjunction of a proposition r and its negation (Â¬r). In classical logic, a contradiction occurs when a statement and its negation are both true. In this case, if r is true, then (Â¬r) is false, and if r is false, then (Â¬r) is true. Therefore, the formula râˆ§(Â¬r) is always false, making it a contradiction.

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Layth Slewa |Cyber Security |
Layth, a passionate and professional technical consultant in Mobile Communications and Cyber Security, combines expertise to excel in these crucial fields.

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• Current Version
• Mar 22, 2023
Quiz Edited by
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• Jan 08, 2015
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