#Discrete math, sets

46 messages · Page 1 of 1 (latest)

unkempt ravine
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Is this a correct way to disprove the statement?

image.png
lapis stone
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in fact there are no correct ways to disprove the statement

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did it ask you to do that?

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or to prove or disprove?

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both the math and the language don't make sense

unkempt ravine
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explain?

lapis stone
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what did the question ask you to do

unkempt ravine
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to prove or disprove the statement

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not formally just with language

lapis stone
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everything about it is weird, like why is "by the definition of an element and subset" in the first bullet

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the second bullet just makes no sense like idek what to say

unkempt ravine
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but this is not true for ∈ since the whole set is an element of another

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basically A does not = {A} yes?

merry mauve
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In the picture above, A is an element of C.

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So you've got
True → True
Which isn't useful for a disproof

unkempt ravine
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Okay can you clarify what i wrote above though?

merry mauve
unkempt ravine
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so the statement is false correct?

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are both false

image.png image.png
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Suppose that A, B and C are sets. For each of the following statements either prove it
is true or give a counterexample to show that it is not" is this question

merry mauve
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I won't spoil the proof, but I will say that the original picture is actually a true statement

unkempt ravine
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how so?

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A /= {A}

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I thought

merry mauve
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I don't follow why it should matter to the statement though

unkempt ravine
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okay, say A = {1}

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if A is an element of B, then B = { {1}, 2, ...}

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then for the case where B is a subset of C, C = { {1}, 2, 3, 4 ...}

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A is not included in C because 1 /= {1}

merry mauve
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A is an element of C

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There's a {1} right there

unkempt ravine
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{1} is a set containing 1

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not 1 itself

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is that incorrect?

merry mauve
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That's a good observation!

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A is also a set containing 1

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One of C's elements is a set containing 1

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A is an element of C

unkempt ravine
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AH okay, however if B is an element of C, then A is not in C

merry mauve
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Yeah the second one you posted is false

unkempt ravine
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thank you, i understand now

vagrant karma
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use the definition of a subset

languid leaf
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.solved