# "If and only if" vs. "if" or "only if", what’s the difference?

By
Greg Smith

Formal logic including conditional or IF-Then statements appear in 3 out of 4 LSAT test sections. Both Logical Reasoning Sections and the Analytical Reasoning Section will use formal logic. This often includes conditional statements such as “IF Bob is selected THEN Suzie is also selected” or “Suzie is selected IF Bob is selected”

How does this statement differ from “Suzie is selected IF, AND ONLY IF Bob is selected”.

IF AND ONLY IF, is a biconditional statement, meaning that either both statements are true or both are false. So it is essentially and “IF” statement that works both ways.

So our statement “Suzie is selected IF, AND ONLY IF, Bob is selected” means that Suzie and Bob are either both selected or both not selected. There are a variety of standard logical symbols used to represent this relationship including:

“↔”, “⇔” and “≡”, and “iff”

For the purpose of diagramming your LSAT Logic Games we recommend the following:

Note that IF AND ONLY IF is different than simply ONLY IF.

Only If simply creates the reverse statement as if you used “IF”

So the statement “IF Mary is selected then Will is also selected” is the same as “Mary is selected ONLY IF Will is also selected” or “ONLY IF Will is select, is Mary selected”

All of which can be respresented as:

IF M –> W

April 10, 2009

### Start our LSAT course now

Learn anytime from anywhere and replay the course at your own pace

50+ HD Video Lessons and Tutorials
12 months subscription for only \$389
Actual LSAT exams and practice questions

# Heading 1 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique.

## Heading 2Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

### Heading 3Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

#### Heading 4Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

##### Heading 5Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.
###### Heading 6Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus, mi quis viverra ornare, eros dolor interdum nulla, ut commodo diam libero vitae erat. Aenean faucibus nibh et justo cursus id rutrum lorem imperdiet. Nunc ut sem vitae risus tristique posuere.

This is some text inside of a div block.
This is some text inside of a div block.
This is some text inside of a div block.
filter by topic

# This is an H1

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

## This is an H2

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

### This is an H3

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

#### This is an H4

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

##### This is an H5

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

###### This is an H6

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

The rich text element allows you to create and format headings, paragraphs, blockquotes, images, and video all in one place instead of having to add and format them individually. Just double-click and easily create content

#### This is an un-ordered list

• This is an item
• This is an item
• This is an item
• This is an item
• This is an item
• This is an item

#### This is an ordered list

1. This is an item
2. This is an item
3. This is an item
4. This is an item
5. This is an item
6. This is an item