23 Sep '03 14:53

In each case, I will define a set of statements (though in some cases the definition may be paradoxical, in which case you should point this out). What can you say for certain about the veracity of the statements?

A: consists of the elements 1 to 5, where n is the statement 'At most n elements of A are true.'

B: consists of the elements 1 to 6, where n is the statement 'At most n elements of B are true.'

C: consists of the elements 1,2,3,4,.... , where n is the statement 'At most n elements of C are true.'

D: consists of the elements 1 to 5, where n is the statement 'At most n elements of D are false.'

E: consists of the elements 1,2,3,4,.... , where n is the statement 'At most n elements of E are false.'

Note: If resident logicians find these too easy, then please give others a chance to answer before you jump in.

A: consists of the elements 1 to 5, where n is the statement 'At most n elements of A are true.'

B: consists of the elements 1 to 6, where n is the statement 'At most n elements of B are true.'

C: consists of the elements 1,2,3,4,.... , where n is the statement 'At most n elements of C are true.'

D: consists of the elements 1 to 5, where n is the statement 'At most n elements of D are false.'

E: consists of the elements 1,2,3,4,.... , where n is the statement 'At most n elements of E are false.'

Note: If resident logicians find these too easy, then please give others a chance to answer before you jump in.