## What is propositional logic with examples?

Definition: A proposition is **a statement that can be either true or false; it must be one or the other, and it cannot be both**. EXAMPLES. The following are propositions: – the reactor is on; – the wing-flaps are up; – John Major is prime minister.

## Which of the following statement is true about propositional logic?

Which of the following statement is true about propositional logic? Answer: **Categorical logic is a part of propositional logic**.

## What operators are used in propositional logic?

**1.1: Propositional Logic**

- A proposition is a statement which is either true or false. …
- But English is a little too rich for mathematical logic. …
- The operators ∧, ∨, and ¬ are referred to as conjunction, disjunction, and negation, respectively.

## What is the notation of if you get more doubles than any other player you will lose or that if you lose you must have bought the most properties?

Represent the statement in symbols as **(P→Q)∨(Q→R)**, where P is the statement “you get more doubles than any other player,” Q is the statement “you will lose,” and R is the statement “you must have bought the most properties.” Now make a truth table.

## How do you write a statement in propositional logic?

For example, in terms of propositional logic, the claims, “if the moon is made of cheese then basketballs are round,” and “if spiders have eight legs then Sam walks with a limp” are exactly the same. They are both implications: statements of the form, **P→Q.** **P → Q** .

## What is a statement in propositional logic?

Propositions. Because propositions, also called statements, are **declarative sentences that are either true or false, but not both**. This means that every proposition is either true (T) or false (F).

## Are the statements P → Q ∨ R and P → Q ∨ P → are 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.

## Which is logically equivalent to P ↔ Q?

P → Q is logically equivalent to **¬ P ∨ Q** . Example: “If a number is a multiple of 4, then it is even” is equivalent to, “a number is not a multiple of 4 or (else) it is even.”

## What does P → Q mean?

p → q (p implies q) (if p then q) is **the proposition that is false when p is true and q is false and true otherwise**. Equivalent to —not p or q“ Ex. If I am elected then I will lower the taxes.

## Which of the proposition is p ∧ (~ p ∨ q is?

The proposition p∧(∼p∨q) is: **a tautology**. **logically equivalent to p∧q**.

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force match |
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## Is {[( P ∧ Q → R → P → Q → R )]} tautology?

<br> Thus, **`[(p to q) ^^(q to r) ] to ( p to r)` is a tautolgy**. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

## Which of the following propositions is tautology Pvq → Qpv Q → P PV P → Q Both B & C?

The correct answer is option (d.) **Both (b) & (c)**. Explanation: (p v q)→q and p v (p→q) propositions is tautology.

## Which of the proposition is p (~ Pvq is a Tautulogy a contradiction logically equivalent to p q All of above?

Which of the proposition is p^ (~ p v q) is

1) | A contradiction |
---|---|

2) | A tautulogy |

3) | All of above |

4) | Logically equivalent to p ^ q |

5) | NULL |

## Which of the following statement is a proposition 2 points a get me a glass of milkshake b God bless you c The only odd prime number is 2 d What is the time now?

(**Option d**) is the correct answer to the given question: The only prime number that is odd is 2. A proposition is a declarative statement in mathematics that gives a clear inference of whether a sentence is true or false.

## Which of the following statement is not a proposition *?

Solution: (3) **Mathematics is interesting**

Mathematics is interesting is not a logical sentence. It may be interesting for some people but may not be interesting for others. Therefore this is not a proposition.