# Suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE. [closed]

I got the first few, but im not sure about these:

1. {2,4}⊂A×A.

2. {∅} ∈ P(A).

3. (1,1)∈A×A.

## closed as off-topic by Eevee Trainer, Henning Makholm, Jyrki Lahtonen, Jean-Claude Arbaut, CesareoApr 22 at 9:36

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• Please tell us your thoughts so we can help you better. – rogerl Apr 22 at 0:35
• I think 7 and 8 is true. Not sure abt 6. – ionics Apr 22 at 0:45
• It is a set.... – ionics Apr 22 at 0:46
• Alright, that solves it. Thanks! – ionics Apr 22 at 0:50
• @ionics Actually, my mistake. $A\times A = \{ (a, b) | a, b\in A\}$. But the point still stands, $A\times A$ is a set of ordered pairs, so a set of numbers cannot be a subset of it – Andrew Li Apr 22 at 0:55

## 1 Answer

$$6)F, 7)F, 8)T$$.

$$6)$$: the elements of $$A×A$$ are ordered pairs, of the form $$(x,y)$$, where $$x,y\in A$$.

$$7)$$: $$\emptyset\in P(A)$$, for any set $$A$$, but $$\{\emptyset\}\neq\emptyset$$, and $$\{\emptyset\}\not\in P(A)$$ for this $$A$$.

$$8)$$: see $$6)$$.

• the element (2,4) belongs to $A$x$A$ but the set {2,4} does not belong to $A$x$A$ is this what you had in mind when you say 6 is false? Thanks. – NoChance Apr 22 at 4:45
• Yeah. That's right. $\{2,4\}$ is neither an element nor a subset of $A×A$. We need ordered pairs. – Chris Custer Apr 22 at 4:49
• I appreciate your clarification. Thanks. – NoChance Apr 22 at 4:49
• Sure thing. @NoChance – Chris Custer Apr 22 at 4:52