Determine if the following statements are true or false: 1. There is exactly one two-digit number...

Determine if the following statements are true or false:

1. There is exactly one two-digit number (in the range from 10 through 99} that is congruent to 1 modulo 3, to 3 modulo 4, and to 3 modulo 5.

2. A minimum element for a partial order R on a set X is an element a such that for every element b, R(a, b) is true. If X is a nonempty finite set, then there must be exactly one minimum element for R.

3. If a and b are any two positive naturals, then the set {a + bi: i is a natural} contains infinitely many prime numbers.

4. There are exactly 32 numbers in the range from 0 through 95 that have inverses modulo 96.

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Expert Solution

Colby Messinger answered 1 year ago

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