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- SUPPOSE ALBERS ELEMENTARY SCHOOL HAS 34 TEACHERS
AND BOTHAL ELEMENTARY SCHOOL HAS 54 TEACHERS.
IF 22 TEACHERS TEACH AT BOTH ALBERS AND BOTHAL
COMPUTE THE TOTAL NUMBER OF TEACHERS
EMPLOYED AT ALBERS OR BOTHAL COMBINED.
LET'S SOLVE THIS USING A VENN DIAGRAM
WHERE SET "A" REPRESENTS THE SET OF TEACHERS THAT TEACH AT ALBERS
AND SET B REPRESENTS THE SET OF TEACHERS THAT TEACH AT BOTHAL.
NOTICE HOW WE'RE TOLD
THAT 22 TEACHERS TEACH AT BOTH SCHOOLS
WHICH MEANS THERE WILL BE 22 TEACHERS
IN THE INTERSECTION OF SET "A" AND B OR THIS REGION HERE.
SO WE HAVE 22 TEACHERS HERE.
NOW WE'RE ALSO TOLD THAT ALBERS HAS 34 TEACHERS
WHICH MEANS THERE ARE 34 TEACHERS IN SET "A,"
BUT NOTICE HOW 22 OF THE 34 ARE ALREADY ACCOUNTED FOR HERE
AND THEREFORE, 34 - 22 WILL GIVE US THE NUMBER OF TEACHERS
THAT ONLY TEACH AT ALBERS
WHICH WILL BE THE NUMBER OF TEACHERS IN THIS REGION HERE.
THESE TEACHERS IN THIS REGION ONLY TEACH AT ALBERS
AND SINCE 34 - 22 IS = 12,
WE KNOW THERE ARE 12 TEACHERS THAT ONLY TEACH AT ALBERS.
NOW USING THE SAME REASONING
WE'RE GOING TO DETERMINE HOW MANY TEACHERS
ONLY TEACH AT BOTHAL.
NOTICE THAT BOTHAL HAS 54 TEACHERS
BUT 22 OF THOSE ALSO TEACH AT ALBERS AND THEREFORE,
54 - 22 WILL GIVE US THE NUMBER OF TEACHERS
THAT ONLY TEACH AT BOTHAL,
WHICH WILL BE THE NUMBER OF TEACHERS IN THIS REGION HERE.
AND SINCE 54 - 22 = 32,
WE KNOW THERE ARE 32 TEACHERS IN THIS REGION HERE.
NOW WE HAVE ALL THE INFORMATION WE NEED.
WE CAN NOW DETERMINE THE NUMBER OF TEACHERS
EMPLOYED AT ALBERS OR BOTHAL COMBINED,
USING SET NOTATION.
THIS WOULD BE THE NUMBER OF ELEMENTS.
IN THIS CASE, THE NUMBER OF TEACHERS IN "A" UNION B,
MEANING SET "A" OR B,
WHICH WOULD BE EQUAL TO 12 + 22 + 32 = 66,
AND THEREFORE,
THERE ARE A TOTAL OF 62 TEACHERS EMPLOYED AT ALBERS OR BOTHAL.
I HOPE YOU FOUND THIS HELPFUL.