WEBVTT
00:00:00.890 --> 00:00:03.380
Decide whether the conclusion is valid.
00:00:04.780 --> 00:00:29.120
Given, if two angles in a triangle add up to 70 degrees, then the triangle is obtuse, and given, the triangle π΄π΅πΆ is an obtuse triangle, the conclusion being two of the angles in the triangle π΄π΅πΆ add up to 70 degrees, is the conclusion valid or not?
00:00:30.120 --> 00:00:33.220
First, we need to consider our two given statements.
00:00:33.910 --> 00:00:40.550
When weβre using if-then statements, we sometimes use the letters p and q to represent the arguments.
00:00:41.730 --> 00:00:50.910
Here p would be if two angles in a triangle add up to 70 degrees, and q would be the triangle being obtuse.
00:00:51.540 --> 00:00:56.810
In conditional statements like these, p is a subset of q.
00:00:57.490 --> 00:01:04.330
We have a large group q, and within that group q falls the subset p.
00:01:05.170 --> 00:01:15.640
Our q is obtuse triangles, and our subset, our conditional p, is triangles whose two angles add up to 70 degrees.
00:01:16.440 --> 00:01:28.720
What weβre not saying is that q, obtuse triangles, and p, triangles whose two angles add up to 70 degrees, fall in the same set.
00:01:29.900 --> 00:01:34.830
Our first statement models this, p being a subset of q.
00:01:36.040 --> 00:01:42.480
Now our second statement says π΄π΅πΆ is an obtuse triangle.
00:01:43.320 --> 00:01:45.640
We have no more information than that.
00:01:46.730 --> 00:01:54.300
In our Venn diagram, we put triangle π΄π΅πΆ in the larger subset of obtuse angles.
00:01:55.180 --> 00:02:05.900
Just because triangle π΄π΅πΆ is an obtuse triangle, that does not automatically make its two angles add up to 70 degrees.
00:02:06.720 --> 00:02:09.360
We would need more information to determine that.
00:02:10.440 --> 00:02:22.390
Concluding that two of the angles in triangle π΄π΅πΆ add up to 70 degrees based on only the information weβre provided is not a valid conclusion.