Compound Statement Math Examples

A statement is any declarative sentence which is either true or false. A square has four sides.

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If 18486 is divisible by 18 then 18486 is divisible by 9.

Compound statement math examples. A compound statement is a sentence that consists of two or more statements separated by logical connectors. A compound statement is a contingent if there is T beneath its main connective in at least one row of its truth table and an F beneath its main connective in at least one row of its truth table. A statement is atomic if it cannot be divided into smaller statements otherwise it is called molecular.

2 2 4. The five logical connectives are. Our examples I will give you 5 or I will not give you 5 and It will either snow today or it will not snow today are very simple.

Consequently P is true. Quadrilaterals have 11 sides. There are for different operations that I will be showing.

A person is a father. Let P be the proposition 2 is even and let Q be the proposition The earth revolves around the sun. The two statements quoted above are simple statements.

The moon is made of cheese. The statement after the is called the ___ consequent ___. A com- bination of two or more simple statements is a compound statement.

For example It is snowing and I wish that I were out of doors but I made the mistake of signing up for this course is a compound statement. Compound Statement Math Examples. The only way for a disjunction to be a false statement is if both halves are false.

All squares are rectangles or quadrilaterals have 11 sides. Salt Lake City is in Utah Q. Here both a and b are true.

This lesson shows you how to use different connectives to write compound statements in set logic. Example 6 Transitivity Here is an example. A disjunction is true if either statement is true or if both statements are true.

Then the sentence P or Q is true since at least one of the sentences P and Q is true. The connective Or can either be inclusive or exclusive. All sides of a square are equal.

Examples of compound statements. 42 is a perfect square. In fact what if we did not have even the English words but started with just the.

Secondly which compound statement is true. P W P W P T T T F F T F T F F F T T T T F F F F T 3. This is the negation of the statement all birds can fly.

Here are examples of writing if-then statements in symbolic form. Telephone numbers in the USA have 10 digits. Represent the following simple statements.

In fact both sentences are true in this case. Statements or propositional variables can be combined by means of logical connectives operators to form a single statement called compound statements. These are statements in fact atomic statements.

Here the connector and was used to create a new statement. In Example 1 each of the first four sentences is represented by a conditional statement in symbolic form. The statement before the is called the___ antecedent ____.

A tautology is a compound statement which is true for every value of the individual statements. Compound statement Math Goodies Glossary. It is easier to determine the truth value of such an elaborate compound statement when a truth table is constructed as shown below.

No matter what the compound statement always leads to a true result so the statement is a tautology. As both the component statements are true mathematically therefore the statement P is also true. If P Q are the statements P.

Finally fill in the p q p q column by considering the truth table for an and statement together with the computed truth values for p q and p q. In the statement Or is used as a connective if each of the statements is true then P is true. This means that the exclusive or statement P or Q but not both is false.

1 1 2 and All birds can fly. Contains two smaller statements. For example the entry for p q in the first row is F because in the first row the truth value of p q is T.

For example compound statement x 1. The time is correct. What about a logic statement that is a bit more complicated.

This statement joins two different mathematically acceptable statements and takes the connective and. The length and breadth of a rectangle are 3 and 6 respectively. P ν q.

Write each compound statement below in symbolic form. A person is a male. Given two statements P Q the compound statement P and Q called the conjunction is denoted by P Q and is defined by the following truth table.

Example Willard is either a philosopher or a windbag and hes not a philosopher. India is in Asia q. It is not the case that all birds can fly.

_ p q _ a. The clock is slow. Let us take another example to understand it in a better way.

I am taking a math class but Im not a math major If I pass MGF1106 and I pass MGF1107 then my liberal studies math requirement will be fulfilled EQUIVALENT STATEMENTS Any two statements p and q are logically equivalent if they have exactly the same meaning. In item 5 p qr is a compound statement that includes the connectors and. Conjunction And Disjunction Examples.

The word tautology is derived from a Greek word where tauto means same and logy means logic. The statements are done one after the other from the beginning to the end. Compound Statement Using Connective Or i If any of the component statements connected by Or is true then the given compound statement is also true.

If we split this statement into component statements we have. If 18486 is divisible by 9 then the sum of the digits of 18486 is divisible by 9. If 18486 is divisible by 18 then the sum of the digits of 18486 is divisible by 9.

P Q P Q T T T T F F F T F F F F Note that the conjunction P Q is true only when both P and Q are true. A compound statement is made with two more simple statements by using some conditional words such as and or not if then and if and only if. If we link one true and one false statement into a compound statement using the connector or symbolized by we still have a true compound statement.

The clock is slow or the time is correct.

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