Logic problems using conditionals

Aim: How Can we solve logic problems using conditionals?

Conditional: The conditional is the most frequently used statement in the construction of an argumet or in the study of mathematics.
* There are four Conditionals that can be formed:
-The Conditional and Biconditional
-The Inverse
-The Converse
-The Contrapositive 

Inverse:Formed by negating the hypothesis and conclusion:
Example:
-The Conditional: "If I study then i will pass the test."
-The Inverse: " If I do not study then I will not pass the test."
                 
What is the inverse of the following statements:
1. "If you do not take a shower than you will stink."    
Answer:
Highlight this using mouse:   -If you do take a shower than you will not  stink  
2. "If Lily is ten years older than Shane who is six then Lily is sixteen."
Answer:
Highlight this using mouse:  If Lily is not ten years older than Shane who is six then Lily is not sixteen.


Converse: Is switching the hypothesis and conclusion.
Example:
 -The Conditional: "If I go into the deep end of the pool i will drown."
-The Converse: "If I drown then ii went into the deep end of the pool."
* When both the conditional and the converse are both true it is called a biconditional.

What is the Converse of the following statement:
1.The Conditional: "If I hate oranges than I will not drink orange juice." 
Answer: 
Highlight this using mouse:"If I do not eat orange juice than I hate oranges" 

Biconditional: Is connecting the hypothesis and conclusion together using the statement If and only if.
Example:
-The Conditional: "If today is Sunday then tomorrow is Monday"
-The Biconditional: "Tomorrow will be Monday if and only if today is Sunday" 

What is the Biconditional of the following statement:
The Conditional: "If you have two pies and add two more pies then you will have four pies"
Answer: 
Highlight this with your mouse:You will have four pies if and only if you have two pies and add two more pies.
Contrapositive:  A cotrapositive is nagating and switching the hypothesis and conclusion; which is basically the combination of the two contrapositives of converse and inverse.
Example; 
-The Conditional:"If i eat ice cream then it will be cookies and cream flavor."
-The Contrapositive: "If I do not have cookies and cream flavor then i will not eat ice cream"  

What is the Contrapositive of the following statements:
1. The conditional"If I have pencils then i will be able to take the test."
Answer:
Highlight this using mouse: "If I am not able to take the test then I do not have pencils."
 2.
The Conditional:"If I have a swimsuit then I am going to the beach"
Answer:
Highlight this: "If I do not go to the beach then I do not have my swimsuit"

TRY IT YOURSELF:
What is the Inverse, Converse, Biconditional, and Contrapositive of the following Statement: 
"If Their is thunder then there is lightning"
Answer:
 Highlight this using mouse: Inverse: "If their is no thunder then there is no lightning"

                                         Converse: "If their is lightning then there is thunder"

                                         Biconditional: "Their is thunder if and only if there is lightning"

                                         Contrapositive:"If their is no lightning then there is no thunder"