#🤗Please Probe my Proof: Did I do this the right way? I feel skeptical

27 messages · Page 1 of 1 (latest)

hybrid tide
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Suppose x ∈ A ⋂ B. Suppose x -∈ C. Then x ∈ A ⋂ B \ C,which contradicts the fact that A and B \ C are disjoint. Therefore,x ∈ C.
(For problem 2 in the screenshot.)
How could we have done this proof better and why?
Is it correct?
What is an alternative method to prove it,and what are the proof strategies behind it?
Thank you 🤗

IMG_8342.png
opal flameBOT
hybrid tide
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From the given disjoint fact,I inferred in my givens that:

-∃x(x ∈ A ⋂ B \ C)

[And since x not in C implied there existed such an x,that’s where I got my contradiction.]

Could I have used existential instantiation explicitly here? Did I already do it by introducing the arbitrary element x?

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This plomble is from the proofs involving quantifiers section of my book,hence why i am skeptical: I don’t think I explicitly used existential/universal instantiation or much of what was taught,like introducing a new variable

idle rover
hybrid tide
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Is the proof wrong?

idle rover
hybrid tide
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I’m afraid I’m not that knowledgeable in set theory,I don’t know what the complement is

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I only know up to power sets and set families

bronze hawk
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Is that ncert?

hybrid tide
halcyon yew
hybrid tide
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So no,it’s not ncert

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<@&286206848099549185> Proof Patrol

noble bone
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https://mathworld.wolfram.com/Complement.html

Complement -- from Wolfram MathWorld

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of the original set. The notations F^' and F^_ are commonly used to denote the complement of a set F. This concept is commonly used and made precise in the particular cases of a ...

noble bone
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search this for 'proof by contraposition'

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or find a way that doesn't assume x ∈ A ⋂ B and x -∈ C

limpid stratus
hybrid tide
noble bone
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not sure, idk what disjoint means

hybrid tide
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/solved

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.solved