Question

Problem 1. [35 Points] Use logical reasoning to prove the following statements. Note that you can only use the rules in Table 3.2.1 in chapter 3 in the book, DeMorgan's law, contrapositive rule that has this format: A$\rightarrow$B $\neg$B$\rightarrow$$\neg$A and a new rule that's called Conditional Simplification that has this format: A$\rightarrow$B$\land$C $\therefore$ A$\rightarrow$B (Note that both rules can be proved by laws of propositional logic.) a) [15 Points] p$\rightarrow$(q$\land$r) s$\rightarrow$r r$\rightarrow$p $\therefore$ s$\rightarrow$q b) [20 Points] $\neg$r$\rightarrow$$\neg$s p$\rightarrow$u $\neg$t$\rightarrow$$\neg$r u$\rightarrow$s t$\rightarrow$q $\therefore$ p$\rightarrow$q

          Problem 1. [35 Points] Use logical reasoning to prove the following statements. Note that you
can only use the rules in Table 3.2.1 in chapter 3 in the book, DeMorgan's law, contrapositive rule
that has this format:
A$\rightarrow$B
$\neg$B$\rightarrow$$\neg$A
and a new rule that's called Conditional Simplification that has this format:
A$\rightarrow$B$\land$C
$\therefore$ A$\rightarrow$B
(Note that both rules can be proved by laws of propositional logic.)
a) [15 Points]
p$\rightarrow$(q$\land$r)
s$\rightarrow$r
r$\rightarrow$p
$\therefore$ s$\rightarrow$q
b) [20 Points]
$\neg$r$\rightarrow$$\neg$s
p$\rightarrow$u
$\neg$t$\rightarrow$$\neg$r
u$\rightarrow$s
t$\rightarrow$q
$\therefore$ p$\rightarrow$q

Problem 1. [35 Points] Use logical reasoning to prove the following statements. Note that you
can only use the rules in Table 3.2.1 in chapter 3 in the book, DeMorgan's law, contrapositive rule
that has this format:
A→B
B→A
and a new rule that's called Conditional Simplification that has this format:
A→BC
∴ A→B
(Note that both rules can be proved by laws of propositional logic.)
a) [15 Points]
p→(qr)
s→r
r→p
∴ s→q
b) [20 Points]
r→s
p→u
t→r
u→s
t→q
∴ p→q

Added by Thomas K.

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