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# Logical Operators

## What Are Logical Operators

Logical operators are symbols that help write out a logical sentence using expressions instead of words. Weâve already seen how we can represent the propositions in phrases with variables such as replace âIt is rainingâ with A and âI wear my raincoatâ with B.

You can think of logical operators like the signs we use when weâre putting together math problems. So when we say 2+3=5 then we could write this A+B=C where A=2, B=3, C=5 and the operators would be the plus(+) sign and the equal(=). These operators tell us certain things about what is going on in the problem. In the math equation the plus signs represents adding number together while the equal sign represents that both sides of the equation should be the same. The following pages will show you what these operators are and how they can be used.

Whenever you write out a series of propositions and operators then the combined formula is known as a statement. These statements can be either True or False. So looking at our math example of 2+3=5 we would say that this statement is true, while the statement 2+2=5 would be false.

There are numerous logical operators but the main ones you will need to know are implications, conjunctions, disjunctions, and negations. In the following sections we will deal with each of these operators and how truth tables can be used to better understand them.