Discrete Mathematics Quiz By: Layth Adeeb

1. A statement that is always true

Tautology

Contradiction

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.

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.

2. "Please Charge my Phone" choose one of the following answers

It is a Statement

It is a Proposition

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

The Truth Value of the proposition is True

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.

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.

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

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.

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.

Submit

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

Because the Value of x is greater than y

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

Because the Value of x is less than y

Because x and y are variables

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.

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.

5. Which of the following formulas Belong to the Contradiction

R∨(¬r)

R∧(¬r)

¬(¬(p∧q)↔(¬p)∨(¬q))

¬(p∧q)↔(¬p)∨(¬q)

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

Explanation

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

6. "Baghdad is the Capital of Iraq" choose all that apply

It is a Statement

The Truth Value of the Proposition is True

The Truth Value of the Proposition is False

It is a proposition

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.

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.

Submit