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If and only if, if but only if, explained

By 
Greg Smith

Here’s a quick video tip on how to set up the following conditional statements including the contrapositive for each:

  • if A then B
  • A if and only if B
  • A if but only if B
  • if and only A then B
  • if but only A then B

April 15, 2010
ABOUT THE AUTHOR

Greg Smith

Greg took the LSAT in 2002 receiving a high score that got him into the law school of his choice. This led him to teach LSAT classes while attending law school at the University of British Columbia and continued teaching while practicing law with top international law firms Borden Ladner Gervais LLP and later Blake Cassels & Graydon LLP, in the area of Securities and Capital Markets. Read more


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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.

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