# (b) Make truth table for followings. (4) i) p→(~r  q)  (~p  r) ii) p→ (~r  ~ q)  (p  ~ r)

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Let's create truth tables for the given logical expressions:

i) $$p \rightarrow (\neg r \land q) \land (\neg p \lor r)$$:

$\begin{array}{cccccccc} p & q & r & \neg r & \neg p & \neg r \land q & \neg p \lor r & (\neg r \land q) \land (\neg p \lor r) & p \rightarrow (\neg r \land q) \land (\neg p \lor r) \\ \hline T & T & T & F & F & F & T & F & F \\ T & T & F & T & F & T & T & T & T \\ T & F & T & F & F & F & T & F & F \\ T & F & F & T & F & F & T & F & F \\ F & T & T & F & T & F & T & F & T \\ F & T & F & T & T & T & T & T & T \\ F & F & T & F & T & F & T & F & T \\ F & F & F & T & T & F & T & F & T \\ \end{array}$

ii) $$p \rightarrow (\neg r \lor \neg q) \lor (p \land \neg r)$$:

$\begin{array}{cccccccc} p & q & r & \neg r & \neg q & \neg r \lor \neg q & p \land \neg r & (\neg r \lor \neg q) \lor (p \land \neg r) & p \rightarrow (\neg r \lor \neg q) \lor (p \land \neg r) \\ \hline T & T & T & F & F & F & F & F & T \\ T & T & F & T & F & T & T & T & T \\ T & F & T & F & T & T & F & T & T \\ T & F & F & T & T & T & T & T & T \\ F & T & T & F & F & F & F & F & T \\ F & T & F & T & F & T & F & T & T \\ F & F & T & F & T & T & F & T & T \\ F & F & F & T & T & T & F & T & T \\ \end{array}$

In both truth tables, $$T$$ represents "True," and $$F$$ represents "False." The final column represents the truth value of the respective logical expressions.