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Home > College Algebra calculators > Mathematical Logic, truth tables, logical equivalence calculator
Method and examples
Mathematical Logic, truth tables, logical equivalence
1. Prepare the truth table
Logical Expression
  
  1. `p vv q`
  2. `p ^^ q=q ^^ p`
  3. `(p vv q) vv r=p vv (q vv r)`
  4. `(p ^^ q) ^^ r=p ^^ (q ^^ r)`
  5. `~(p vv q)=~p ^^ ~q`
  6. `~(p ^^ q)=~p vv ~q`
  7. `p ^^ (q vv r)=(p ^^ q) vv (p ^^ r)`
  8. `p vv (q ^^ r)=(p vv q) ^^ (p vv r)`
  9. `p ^^ (p vv q)=p`
  10. `p vv t=t`
  11. `p ^^ c=c`
  12. `p => q = q => p`
  13. `p <=> q`
  14. `p" nand "q`
  15. `p" nor "q`
  16. `p" xor "q`
2. Examine the logical validity of the argument
Hypothesis
Conclusion
  
  1. Hypothesis : `p or q;"not "p` and Conclusion : `q`
  2. Hypothesis : `(p and" not"(q)) => r;p or q;q => p` and Conclusion : `r`
  3. Hypothesis : `p => q;q => r` and Conclusion : `p => r`
  4. Hypothesis : `p => q;p` and Conclusion : `q`
  5. Hypothesis : `p => q;p => r` and Conclusion : `p => (q and r)`
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