Let k e Z+. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but unspecified element of A). Define X := {X | X C A and a ¢ X} Y:= {Y | Y C A and a e Y} 4. Show that the function...

Let k e Z+. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but<br>unspecified element of A). Define<br>X := {X | X C A and a ¢ X}<br>Y:= {Y | Y C A and a e Y}<br>4. Show that the function f : X → Y defined by<br>f(X) = XU {a} VX €X<br>is a bijection.<br>

Extracted text: Let k e Z+. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but unspecified element of A). Define X := {X | X C A and a ¢ X} Y:= {Y | Y C A and a e Y} 4. Show that the function f : X → Y defined by f(X) = XU {a} VX €X is a bijection.

Jun 05, 2022

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Let k e Z+. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but unspecified element of A). Define X := {X | X C A and a ¢ X} Y:= {Y | Y C A and a e Y} 4. Show that the function...

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