4. Let A = {x1, 2,...,12} be a set with 12 elements. Determine the number of...

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4. Let A = {x1, 2,...,12} be a set with 12 elements. Determine the number of subsets of A that satisfy each of the following conditions, and explain your reasoning. You can write your final answer as a formula like 3. 2¹0 + 4.2¹¹ - 1 rather than computing a number; in fact, that form of solution is preferred. (a) How many subsets include (2, 5, x8, x11} as a subset? (b) How many subsets contain at most one of x2, X5, x8, x11? (c) How many subsets do not contain at least one of x1, x2, x3? (d) The subset contains x₁ or x2, and does not contain ₁1 or does not contain *12? 4. Let A = {x1, 2,...,12} be a set with 12 elements. Determine the number of subsets of A that satisfy each of the following conditions, and explain your reasoning. You can write your final answer as a formula like 3. 2¹0 + 4.2¹¹ - 1 rather than computing a number; in fact, that form of solution is preferred. (a) How many subsets include (2, 5, x8, x11} as a subset? (b) How many subsets contain at most one of x2, X5, x8, x11? (c) How many subsets do not contain at least one of x1, x2, x3? (d) The subset contains x₁ or x2, and does not contain ₁1 or does not contain *12?

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a since every other element can either be or not be there are two possibilities of ever... View the full answer