Create a Euler diagram to determine whether the syllogism is valid or invalid.
Some musicians stay up late.
Greg is a musician.
Greg stays up late.
some do , and some dont.
so it is valid?
hardly. some musicians go to bed early.
greg is a musician, greg goes to bed early.
you have a circle for musicians
you have a circle for staying up late
the circles overlap (musicians who stay up late are in the overlapping zone, the intersection)
in the zone common to the two circles, the intersection, you have Greg.
thank you Damon...the syllogism is invalid correct?
To create a Euler diagram and determine the validity of this syllogism, we can follow these steps:
Step 1: Identify the statements in the syllogism.
- Some musicians stay up late.
- Greg is a musician.
- Greg stays up late.
Step 2: Determine the categories involved.
In this case, the categories are musicians and people who stay up late.
Step 3: Draw the Euler diagram.
- Start by drawing two overlapping circles to represent the categories. Label one circle as "musicians" and the other as "people who stay up late."
- Since the first statement says "Some musicians stay up late," we can represent this by shading a portion of the "musicians" circle that overlaps with the "people who stay up late" circle.
_______
/ \
| |
\_________/
- Next, indicate the second statement that "Greg is a musician" by labeling a point within the "musicians" circle as "Greg."
_______
/ \
| Greg |
\_________/
- Finally, check if the third statement "Greg stays up late" is valid. Since Greg is within the shaded portion of the "musicians" circle, we can conclude that Greg is indeed within the "people who stay up late" category.
_______
/ \
| Greg |
\_________/
Step 4: Determine the validity.
In this case, the syllogism is valid because the conclusion "Greg stays up late" is supported by the premises. Since Greg is a musician, and some musicians stay up late, it logically follows that Greg also stays up late.
Therefore, by following these steps and drawing a Euler diagram, we have determined that the syllogism is valid.