# Shading A Venn Diagram Using A Specific Equation

The expression is: $A\triangle(B\cap C')$. The $\triangle$ refers to $-$ and the $\cap$ refers to an intersection, whilst the $\;{}'$ refers to the prime of $C$.

There are no numbers or items included in this problem. I have drawn a Venn diagram with a background (for the universal set) and circles $A$, $B$ and $C$ which equally overlap. The problem is, I am unsure how to shade it. I also must provide the logic used to solve the equation. Thanks a bunch!

It might help to do this in steps, from the inside out, try drawing tree diagrams:

• in the first, simply shade C', that is all the area out side of $C$.
• next, you'd like to draw $B\cap C'$ i.e. the intersection of $B$ with the shaded area of the previews diagram, more simply it would be the area inside $B$ that was shaded in the first diagram.
• finally, in the third diagram, you need to shade the area inside A that was not shaded in the second diagram.

put into words the expression means, everything that is in A with the exception of($\Delta$) things that are in B and($\cap$) not($′$) in $C$.

At first this might be confusing, and you might need to draw the steps, but with practice you will learn to do it in your head, Venn diagrams are a very powerful tool for intuitively understanding logic.

• This answer was very confusing, but gave me an idea how to solve it. It would have been simpler had I known that A△(B∩C′) is equivalent to A∩(B∩C')' Thanks! – Shayna May 21 '13 at 8:32

A△(B∩C′) = A∩(B∩C')' They are equivalent! So, shade all of A that is not in B. Also shade the intersection of A, B & C (You should have shaded A, A/C AND A/B/C.).
{"ft_lang_label":"__label__en","ft_lang_prob":0.9319738,"math_prob":0.9808967,"size":458,"snap":"2020-10-2020-16","text_gpt3_token_len":118,"char_repetition_ratio":0.11894273,"word_repetition_ratio":0.0,"special_character_ratio":0.27292576,"punctuation_ratio":0.125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986832,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-22T17:25:57Z\",\"WARC-Record-ID\":\"<urn:uuid:ff431ad1-fe2c-48ca-aa36-8f30a18151ed>\",\"Content-Length\":\"145100\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:85ecf287-fbdc-4883-accd-fa2319e54322>\",\"WARC-Concurrent-To\":\"<urn:uuid:8a1c05f5-6605-4db4-8915-37cc0dbf8dff>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/390199/shading-a-venn-diagram-using-a-specific-equation/390218\",\"WARC-Payload-Digest\":\"sha1:YJEDWSWTN3MDEZ3ZLT5RZ7LTPZSMVRGI\",\"WARC-Block-Digest\":\"sha1:QH2Z6DGUDFCAN3AC6PGH6KXWVPOBPCYG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145708.59_warc_CC-MAIN-20200222150029-20200222180029-00310.warc.gz\"}"}