Problem 26E

Suppose that P(n) is a propositional function. Determine for which nonnegative integers n the statement P (n) must be true if

a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n + 2) is true.

b) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n + 3) is true.

c) P(0) and P(1) are true; for all nonnegative integers n. if P(n) and P(n + 1) are true, then P(u + 2) is true.

d) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n + 2) and P(n + 3) are true.

Chapter 4 4.1 Cellular Level of Organization • Detailed study of the cell in the 1830s • A unifying concept in biology • Originated from the work of biologists in 1838–1839 • Cel All organisms are composed of cells. All cells come only from preexisting cells because cells are self-reproducing. Cells are the basic units of structure and function in organisms. Cell size • Cells range in size from one millimeter (mm) down to one micrometer (μm) in diameter. • Cells need a large surface area of plasma membrane to adequately exchange materials. • The surface-area-to-volume ratio requires that cells be small. Large cells – surface area relative to volume decreases which also decrease