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Determine the validity of the following arguments without using truth tables.

Determine the validity of the following arguments without using truth tables.

(a)  If I like mathematics, then I will study.

I will not study.

Either I like mathematics, or I like soccer.  

therefore, I like soccer. 


(b) If I like mathematics, then I will study.

  • Either I do not study, or I pass mathematics.
  • If I do not graduate, then I did not pass mathematics.
  • ∴ If I like mathematics, then I will graduate


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