Let us use laws of logic solve the following compound propositions.
[p∧(¬p∨q)]∨[q∧¬(p∧q)]
| use the distributive law |
=[(p∧¬p)∨(p∧q)]∨[q∧¬(p∧q)]
| use de Morgan law |
=[(p∧¬p)∨(p∧q)]∨[q∧(¬p∨¬q)]
| use the law of contradiction |
=[F∨(p∧q)]∨[q∧(¬p∨¬q)]
| use the distributive law |
=[F∨(p∧q)]∨[(q∧¬p)∨(q∧¬q)]
| use the constant law |
=(p∧q)∨[(q∧¬p)∨(q∧¬q)]
| use the law of contradiction |
=(p∧q)∨[(q∧¬p)∨F]
| use the constant law |
=(p∧q)∨(q∧¬p)
| use the commutative law |
=(q∧p)∨(q∧¬p)
| use the distributive law |
=q∧(p∨¬p)
| use the law of the excluded third |
=q∧T
| use the constant law |
=q
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