# To say that a set Ais tidy means that, for every x, if x is an element of A, thenis a subset of A. Also recall that,for any set X, we have defined the successor ofX, S(X), to be the set XU{X}.1. Suppose that U and V are both tidy. Prove that U n V is tidy.2. Suppose that X is tidy. Prove that S(X) is tidy.

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To say that a set A is tidy means that, for every x, if x is an element of A, then x is a subset of A. Also recall that, for any set X, we have defined the successor of X, S ( X ), to be the set X ∪ { X }.

1. Suppose that U and V are both tidy. Prove that U ∩ V is tidy.
2. Suppose that X is tidy. Prove that S ( X ) is tidy.
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Step 1

Given:

Step 2

Proof:

Step 3

2] Suppose X is t...

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