Introduction to Logic: Level Six Tutorials

Tutorial Contents

Tutorial Six: Predicate Calculus with Identity - TRussell's Theory of Descriptions -
Scope - Tableau Rules for Identity

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One

Exercise 6.1

1.

Using the following interpretation:

	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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