Using truth tables to compare statements.

 

1. Use a truth table to decide each of the following (and explain how you determined each answer):

a) are the statements consistent?
b) does the first statement imply the second?
c) does the second imply the first?
d) are the statements equivalent?

1.h->g

2.h&~g

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2. Use a truth table to decide each of the following (and explain how you determined each answer):

a) are the statements consistent?
b) does the first statement imply the second?
c) does the second imply the first?
d) are the statements equivalent?

1.(r<->s)&~s

2.~rv(~tv~s)

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3. Use a truth table to answer the following questions about the following 3 statements.

a) Are 1-2 consistent with 3?
b) Do any of 1-2 individually imply 3?
c) Do 1-2 jointly imply 3?

1.b->d

2.a

3.a->c

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4. Use a truth table to answer the following questions about the following 4 statements.

a) Are 1-2 consistent with 3?
b) Do any of 1-2 individually imply 3?
c) Do 1-2 jointly imply 3?

1.x&~z

2.zv(x->~x)

3.y->(x->z)

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5. Use a truth table to answer the following questions about the following 4 statements.

a) Are 1-3 consistent with 4?
b) Do any of 1-3 individually imply 4?
c) Do 1-3 jointly imply 4?


1.~a

2.bv(a->~b)

3.cv(b<->a)

4.cv~b

[ solution ]