10. Exploring Propositions. In Progress Check 1.2, we used exploration to show that certain statements were false and to make conjectures that certain statements were true. We can also use exploration...

Please answer question b.

b) Is it possible to formulate a conjecture about the units digit of numbers
of the form 7^2 -  2^n, where n is a natural number? If so, formulate a
conjecture in the form of a conditional statement in the form “If n is a
natural number, then : : :

Extracted text: 10. Exploring Propositions. In Progress Check 1.2, we used exploration to show that certain statements were false and to make conjectures that certain statements were true. We can also use exploration to formulate a conjecture that we believe to be true. For example, if we calculate successive powers of 2 (2', 22, 23, 2ª, 25, ...) and examine the units digits of these numbers, we could make the following conjectures (among others): 000 BY NC SA 16 Chapter 1. Introduction to Writing Proofs in Mathematics • If n is a natural number, then the units digit of 2" must be 2, 4, 6, or 8. • The units digits of the successive powers of 2 repeat according to the pattern "2, 4, 8, 6." (a) Is it possible to formulate a conjecture about the units digits of succes- sive powers of 4 (4', 4², 4³, 4ª, 45, . )? If so, formulate at least one conjecture. (b) Is it possible to formulate a conjecture about the units digit of numbers of the form 7" – 2", where n is a natural number? If so, formulate a conjecture in the form of a conditional statement in the form "If n is a natural number, then ... ."