$**$ Let A and B be true, X$,$ Y$,$ and Z false. P and Q have unknown truth value. Please, determine

the truth value of the propositions in problems $36,37,38,39,40,$ and $41.$ Please, show the

process of calculation by using the letter $$T$$ for $$true$,$F$$ for $$false$,$ and $?$ for $$unknown value$$

under each letter and operator. Please underline your answer $($truth value under the main

operator$)$ and also make it into Bold font.. $($# $36$ and $37$: $0\mathrm{.}3$ points only when the whole

process of truth value calculation is correctly demonstrated to the answer. # $38-41$: $0\mathrm{.}2$ points$)$

$36.[($ Z $$ P $)$ P $]$ P

$37.$ ~ $($ P $$ Y$)$ v $($ Z $$ Q$)$

$38.[$A $$ ~$($ B $$ Y$)]\backslash$Xi ~$[$B $($X $$ ~ A$)]$

a$.$ True

b$.$ False

$39.$ In Problem $38,$ the main operator is a:

a$.$ Tilde

b$.$ Wedge

c$.$ Triple bar

d$.$ Dot

e$.$ Horseshoe

$40.[($X $$ A$)($B $$ ~ Y$)][($B v Y$)($A $$ X$)]$

a$.$ True

b$.$ False

$41.$ In Problem $40,$ the main operator is a:

a$.$ Wedge

b$.$ Tilde

c$.$ Dot

d$.$ Horseshoe

e$.$ Triple bar

PHIL $111$ Introduction to Logic $($Mini $2024)$ Name:

$2$

nd Exam

$8$

$**$ Use ordinary truth tables to answer questions# $42-43(0\mathrm{.}3$ point for each$)$

$42.$ Given the statement $($N $$ K$)\backslash$Xi $($K $$N$)$

a$.$ Contingent

b$.$ Inconsistent

c$.$ Consistent

d$.$ Tautologous

e$.$ Self$-$contradictory

$43.$ Given the pair of statements ~ $($S $$ Q$)$ and ~ Q $$ S

These statements are:

a$.$ Logically equivalent

b$.$ Valid

c$.$ Contradictory

d$.$ Consistent

e$.$ Inconsistent