How Do We Solve Logic Problems Using Conditionals?

In This Post You Will Learn What A Conditional Is & How To Solve Logic Using It.

In logic, a conditional is a compound statement formed by combining two sentences (or facts) using the words "if ... then."

There Are Three Types Of Conditionals & One Special Conditional:

The converse of a conditional statement is formed byinterchanging the hypothesis and conclusion of the original statement. In other words, the parts of the sentence change places. The words "if" and "then" do not move.

Example:

Conditional: "If the space shuttle was launched, then a cloud of smoke was seen."

Converse: "If a cloud of smoke was seen, then the space shuttle was launched."

HINT: Try to associate the logical CONVERSE with Converse™ sneakers -- think of the two parts of the sentence "putting on their sneakers" and "running" to their new positions.

** It is important to remember that the converse does NOT necessarily have the same truth value as the original conditional statement.

The inverse of a conditional statement is formed bynegating the hypothesis and negating the conclusion of the original statement. In other words, the word "not" is added to both parts of the sentence.

Example:

Conditional: "If you grew up in Alaska, then you have seen snow."

Inverse: "If you did not grow up in Alaska, then you have not seen snow."

HINT: Remember that to create an INverse, you will need to INsert the word NOT into both portions of the sentence. Since you are actually negating each part of the sentence, you may also use other words (in addition to NOT) to create the negation.

** It is important to remember that the inverse does NOT necessarily have the same truth value as the original conditional statement.

The contrapositive of a conditional statement is formed bynegating both the hypothesis and the conclusion, and then interchangingthe resulting negations. In other words, the contrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE.

Example:

Conditional: "If 9 is an odd number, then 9 is divisible by 2." (true) (false)	This statement is logically FALSE.
Contrapositive: "If 9 is not divisible by 2, then 9 is not an odd number." (true) (false)	This statement is logically FALSE.

HINT: Remember that the contrapositive (a big long word) is really the combining together of the strategies of two other words: converse and inverse.

**An important fact to remember about the contrapositive, is that it always has the SAME truth value as the original conditional statements.

In logic, a biconditional is a compound statement formed by combining two conditionals under "and." Biconditionals are true when bothstatements (facts) have the exact same truth value.

A biconditional is read as "[some fact] if and only if [another fact]" and is true when
the truth values of both facts are exactly the same
-- BOTH TRUE or BOTH FALSE.

Great You Now Know The Three Different Types Of Conditionals! Create An Inverse, Converse, Bioconditional & Contropositive For The Following Conditional:

"If Mary is eating the pizza, then Mary is hungry."

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Sources:

http://regentsprep.org/Regents/math/geometry/GP2/Lconvers.htm

http://regentsprep.org/regents/math/geometry/GP2/Lcontrap.htm.

http://regentsprep.org/Regents/math/geometry/GP2/Linvers.htm