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Using the Law of Syllogism. With tricky puzzles!. 1 rule:. Since the CONTRAPOSITVE only statement that is guaranteed to be true if the conditional is true, try rewriting the statements in the contrapositive. Think of this like dominos—the ends must match up. Example.

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using the law of syllogism

Using the Law of Syllogism

With tricky puzzles!

1 rule
1 rule:
  • Since the CONTRAPOSITVE only statement that is guaranteed to be true if the conditional is true, try rewriting the statements in the contrapositive.
  • Think of this like dominos—the ends must match up.
example
Example
  • xy, t~y, ~t~q
  • ~y~x, y~t, qt
  • First write the contrapositive of each statement.
  • Second, circle the statements you will use.
  • Then write in order:
  • xy, y~t, ~t~q, therefore xq
example more difficult
Example—more difficult!
  • tq, ~d~q, ~be, d~e, b~a
  • ~q~t, qd, ~eb, e~d, ab
  • Write all the contrapositives
  • Circle the matches
  • Order

Solution: a~b, ~be, e~d, ~d~q, ~qt

Therefore: at

examples
Examples
  • sa, ~cl, h~i, ci, a~l
  • yt, e~g, ~re, r~t
  • Ps, in, ~pa, a~n
solutions
Solutions
  • H~i, ~i~c, ~cl, l~a, ~a~s (H~S)
  • G~e, ~er, r~t, ~t~y (G~Y)
  • ~s~p, ~pa, a~n, ~n~I (~S~i)