(Question 1)(4.5 points) a', b', c', p', q', r', and s' are propositions. --> denotes logical...

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(Question 1)(4.5 points) a', b', c', p', q', r', and s' are propositions. --> denotes logical implication. /\ denotes logical AND. State whether the following statements are true or false, using a T for a true statement and an F for a false statement. (i) (p' V q' V r') is logically equivalent to ~p' --> (q' V r'). (ii) (p' V q' V r') is logically equivalent to ~q' --> (p' V r'). (iii) (p' V q' V r') is logically equivalent to ~r' --> (p' V q'). (iv) (~p' V q' V r') is logically equivalent to p' --> (q' V r'). (v) (~p' V q' V r') is logically equivalent to (p' /\ ~q') --> r'. (vi) (p' V q' V~r' V ~s') is logically equivalent to (r' V s') --> (p' /\ q'). (vii) (p' V q' V-r' V ~s') is logically equivalent to (r' --> q') V (s' --> p'). (viii) (~a' V (b' --> c')) is logically equivalent to ((a' --> b') V c'). (ix) (~a' V (b' --> c')) is logically equivalent to ((a' /\ b') --> c'). (Question 1)(4.5 points) a', b', c', p', q', r', and s' are propositions. --> denotes logical implication. /\ denotes logical AND. State whether the following statements are true or false, using a T for a true statement and an F for a false statement. (i) (p' V q' V r') is logically equivalent to ~p' --> (q' V r'). (ii) (p' V q' V r') is logically equivalent to ~q' --> (p' V r'). (iii) (p' V q' V r') is logically equivalent to ~r' --> (p' V q'). (iv) (~p' V q' V r') is logically equivalent to p' --> (q' V r'). (v) (~p' V q' V r') is logically equivalent to (p' /\ ~q') --> r'. (vi) (p' V q' V~r' V ~s') is logically equivalent to (r' V s') --> (p' /\ q'). (vii) (p' V q' V-r' V ~s') is logically equivalent to (r' --> q') V (s' --> p'). (viii) (~a' V (b' --> c')) is logically equivalent to ((a' --> b') V c'). (ix) (~a' V (b' --> c')) is logically equivalent to ((a' /\ b') --> c').

Answer rating: 100% (QA)

i F ii T iii T iv T v T vi T vii T viii T ix T Explanation i p V q V r is not logically equiva... View the full answer