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- IN THE LAST SEVERAL WEEKS 17 DAYS SAW RAIN
AND 11 DAYS SAW HIGH WINDS.
IN THAT SAME TIME PERIOD,
FOUR DAYS SAW BOTH RAIN AND HIGH WINDS.
HOW MANY DAYS SAW EITHER RAIN OR HIGH WINDS?
WE JUST SOLVED THIS PROBLEM USING A VENN DIAGRAM.
THIS TIME LET'S USE A DEFINITION USED TO DETERMINE
THE NUMBER OF ELEMENTS IN A UNION OF TWO SETS.
SO TO GET US STARTED,
SET R REPRESENTS THE SET OF DAYS THAT SAW RAIN
AND SET W REPRESENTS THE SET OF DAYS THAT SAW HIGH WINDS.
AND THE INTERSECTION OF THESE TWO SETS
REPRESENTS THE SET OF DAYS THAT SAW RAIN AND HIGH WINDS.
SO TO FIND THE NUMBER OF DAYS
THAT SAW EITHER RAIN OR HIGH WINDS,
YOU WANT TO FIND THE NUMBER OF ELEMENTS,
SO IN THIS CASE THE NUMBER OF DAYS,
IN THE UNION OF SET R AND SET W.
THE FORMULA FOR THIS SAYS,
THE NUMBER OF ELEMENTS IN R UNION W
IS EQUAL TO THE NUMBER OF ELEMENTS IN SET R,
WHICH WOULD BE THE NUMBER OF ELEMENTS IN THIS SET HERE
PLUS THE NUMBER OF ELEMENTS IN SET W,
THIS SET HERE,
AND THEN MINUS THE NUMBER OF ELEMENTS IN R INTERSECT W
OR THE NUMBER OF ELEMENTS IN R AND W,
WHICH WOULD BE THE NUMBER OF ELEMENTS IN THIS REGION HERE.
NOW, THE REASON WE HAVE TO SUBTRACT THIS OUT
IS BECAUSE NOTICE HOW WE COUNTED THESE ELEMENTS TWICE,
ONCE IN R AND ONCE IN W,
AND THEREFORE TO FIND
THE NUMBER OF ELEMENTS IN THE UNION,
WE DO HAVE TO SUBTRACT THIS INTERSECTION.
TO APPLY THIS FORMULA FOR OUR SITUATION,
AGAIN WE'RE LOOKING FOR THE NUMBER OF ELEMENTS
IN R UNION W.
WE'LL TAKE THE NUMBER OF ELEMENTS IN SET R,
WHICH IS THE NUMBER OF DAYS THAT SAW RAIN, WHICH IS 17.
ADD THE NUMBER OF ELEMENTS IN SET W
OR THE NUMBER OF DAYS THAT SAW HIGH WINDS, WHICH IS 11,
AND THEN SUBTRACT THE NUMBER OF ELEMENTS IN R INTERSECT W,
WHICH REPRESENTS THE NUMBER OF DAYS
THAT SAW BOTH RAIN AND HIGH WINDS, WHICH IS FOUR.
SO WE HAVE 17 + 11, THAT'S 28 - 4 = 24.
AND THEREFORE WE CAN SAY 24 DAYS SAW RAIN OR HIGH WINDS.
REGARDLESS OF OUR APPROACH,
OF COURSE WE DO GET THE SAME RESULT.
I HOPE YOU FOUND THIS HELPFUL.