Chapter 1.3, Problem 5E

Determine the validity of each of the following arguments. If the argument is one of those listed in the text, name it.

(a)

If I stay up late night, then I will be tired in the morning.

I stayed up late last night.

I am tired this morning.

(b)

If I stay up late at night, then I will be tired in the morning.

I am tired this morning.

I stayed up late last night.

(c)

If I stay up late night, then I will be tired in the morning.

I am not tired this morning.

I did not stay up late last night.

(d)

If I stay up late night, then I will be tired in the morning.

I did not stay up late last night.

I am not tired this morning.

(e)

Either I wear a red tie or I wear blue socks.

I am wearing pink socks.

I am wearing a red tie.

(f)

Either I wear a red tie or I wear blue socks.

I am wearing blue socks.

I am not wearing a red tie.

(g)

If I work hard, then I earn lots of money.

If I earn lots of money, then I pay high taxes.

If I pay high taxes, then I have worked hard.

(h)

If I work hard, then I earn lots of money.

If I earn lots of money, then I pay high taxes.

If I work hard, then I pay high taxes.

(i)

If I work hard, then I earn lots of money.

If I earn lots of money, then I pay high taxes.

If I do not work hard, then I do not pay high taxes.

(j)

If I like mathematics, then I will study.

I will not study.

Either I like mathematics or I like football.

I like football.

(k)

Either I study or I like football.

If I like football, then I like mathematics.

If I don’t study, then I like mathematics.

(l)

If I like mathematics, then I will study.

Either I don’t study or I pass mathematics.

If I don’t graduate, then I didn’t pass mathematics.

If I graduate, then I studied.

(m)

If I like mathematics, then I will study.

Either I don’t study or I pass mathematics.

If I don’t graduate, then I didn’t pass mathematics.

If I like mathematics, then I will graduate.