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## What qualifies a statement as logical?

Logical and Critical Thinking

**A statement is true if what it asserts is the case**, and it is false if what it asserts is not the case. For instance, the statement “The trains are always late” is only true if what it describes is the case, i.e., if it is actually the case that the trains are always late.

## What is an example of a logical statement?

*Here I want to use these exercises to illustrate the idea of a logical statement. Here it says decide whether or not to follow their statement for each that is a statement decide if it is compound and*

## Is a logical statement that is either true or false?

**A proposition** is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0).

## How do you determine whether a proposition is in logical form?

The propositions are equal or logically equivalent **if they always have the same truth value**. That is, p and q are logically equivalent if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa. If p and q are logically equivalent, we write p = q.

## Which of the following is not a logical statement?

**Plants are living objects** is not a statement of logic.

## What is not statement?

In Boolean algebra, the NOT operator is **a Boolean operator that returns TRUE or 1 when the operand is FALSE or 0, and returns FALSE or 0 when the operand is TRUE or 1**. Essentially, the operator reverses the logical value associated with the expression on which it operates.

## Are the statements P ∨ Q → R and P → R ∨ Q → R logically equivalent?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, **the propositions are logically equivalent**. This particular equivalence is known as the Distributive Law.

## How do you know if it is a statement or not?

A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, **a sentence must be true or false, and it cannot be both**. So a sentence such as “The sky is beautiful” is not a statement since whether the sentence is true or not is a matter of opinion.

## What is defined as a sentence that could be either true or false but not both?

**A proposition** is a declarative sentence that is either true or false (but not both).

## Which of the following is NOT logical operator?

! is a NOT operator. So, **‘&’** is not a Logical operator.

## Which of the following is a statement in logic Mcq?

1 Answer. Correct option: (D) **Bombay is the capital of India**. ‘Bombay is the capital of India’ is a statement.

## Which of the following is an open statement?

Solution: (1) **x is a natural number**

“x is a natural number” is an open statement.

## Which of the following is a conditional statement?

The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A truth table for p q is shown below.

Definition: A Conditional Statement is…

p | q | p q |
---|---|---|

F | F | T |

## What is a true false or open equation?

**An equation is true if the expressions on either side of the equal sign are equal**. An equation is false if the expressions on either side of the equal sign are not equal. An equation is an open sentence if it contains one or more variables.

## What does if/p then q mean?

Conditional Propositions – A statement that proposes something is true on the condition that something else is true. For example, “If p then q”* , where **p is the hypothesis (antecedent) and q is the conclusion (consequent)**.

## What is a converse statement?

Definition: The converse of a conditional statement is **created when the hypothesis and conclusion are reversed**. In Geometry the conditional statement is referred to as p → q. The Converse is referred to as q → p.

## When can a conditional statement be false?

A conditional statement is false **if hypothesis is true and the conclusion is false**. The example above would be false if it said “if you get good grades then you will not get into a good college”. If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional.

## What is converse in math?

The converse of a statement is **formed by switching the hypothesis and the conclusion**. The converse of “If two lines don’t intersect, then they are parallel” is “If two lines are parallel, then they don’t intersect.” The converse of “if p, then q” is “if q, then p.”

## What is negation statement?

In Mathematics, the negation of a statement is **the opposite of the given mathematical statement**. If “P” is a statement, then the negation of statement P is represented by ~P. The symbols used to represent the negation of a statement are “~” or “¬”. For example, the given sentence is “Arjun’s dog has a black tail”.

## What is a converse of a conditional statement?

A conditional statement is **logically equivalent to its contrapositive**. Converse: Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p. A conditional statement is not logically equivalent to its converse.

## What is inversion logic?

In logic, an inverse is **a type of conditional sentence which is an immediate inference made from another conditional sentence**. More specifically, given a conditional sentence of the form , the inverse refers to the sentence. .

## What is the meaning of converse inverse and contrapositive?

The converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”

## What is inverse and converse in logic?

If the statement is true, then the contrapositive is also logically true. **If the converse is true, then the inverse is also logically true**.

Converse, Inverse, Contrapositive.

Statement | If p , then q . |
---|---|

Converse | If q , then p . |

Inverse | If not p , then not q . |

Contrapositive | If not q , then not p . |