Introduction to Logic: Level One Exercises

Exercise Contents

Exercise Six: 6.1 - 6.2 - 6.3

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Eight

Exercise 6.1

1.

Using the following interpretation:

	Tableau Rules for Identity Domain: everything in 12 Main Street, Anytown
	a: John
	b: Mary
	Mx: x is a man
	Wx: x is a woman
	Lxy: x likes y
	Hx: x is human

formalise the following:

(i)

There is a least one woman

(ii)

There are at least two women

(iii)

There are at least three women

(iv)

The is at most one woman

(v)

There are at most two women

(vi)

There is exactly one woman

(vii)

There is exactly one woman who likes John

(viii)

Only one person likes both John and Mary.

(ix)

Everyone likes at most one woman who likes only one man.

2.

Using the same interpretation, translate the following into English:

(i)

$xMx

(ii)

$x$y[MxÙMy]

(iii)

$x$y[[MxÙMy]Ù¬x=y]

(iv)

"x"y[[MxÙMy]®x=y]

(v)

¬$x$y[[MxÙMy]Ù¬x=y]

(vi)

¬"x"y[[MxÙMy]®x=y]

(vii)

$x[[WxÙLxa]Ù¬$y[[WyÙLya]Ù¬x=y]]

(viii)

$x[[WxÙLxa]Ù¬$y[WyÙ¬x=y]]

(ix)

$x"y[x=y®My]

(x)

$x"y[My®x=y]

(xi)

$x"y[[WyÙLya]«x=y]

(xii)

$x"y[x=y®Mx]

(xiii)

$x"y[Mx®x=y]

(xiv)

"y$x[x=y®Mx]

(xv)

$x[[Mx Ù"y[Wy®Lyx]]Ù"z[[MzÙ"u[Wu®Luz]]®z=x]

(xvi)

"x[Mx®$y[[WyÙLxy]Ù"z[[WzÙLxz]®z=y]]]

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