Question

1. if a rectangle has four equal sides, then it is a square. if a polygon is a square, then it is a regular polygon.

use the law of detachment and the law of syllogism to draw two conclusions from the following statements.

1. if mickey plays outside, then he will get muddy. if mickey gets muddy, then he needs a bath. mickey plays outside.
2. if two angles form a right angle, then they have a sum of 90. if two angles have a sum of 90, then they are complementary. ∠x and ∠y form a right angle.

use deductive reasoning to answer the following questions.

1. harold, clara, and mark each choose a different lunch from the three categories: soup, salad, and sandwiches. each ordered a different drink. clara will not eat sandwiches. mark won’t eat salad or bread. the person who had the soup also had the iced tea. the person who had the sandwich also had the milk.

a. who drank the milk? how do you know?
b. one person ordered mineral water. what food did the water go with? explain.

Explanation:

14.

Step1: Apply Law of Detachment

Given "If Mickey plays outside, then he will get muddy" and "Mickey plays outside". By the Law of Detachment, we can conclude that Mickey will get muddy.

Step2: Apply Law of Syllogism and Detachment

We have "If Mickey plays outside, then he will get muddy", "If Mickey gets muddy, then he needs a bath" and "Mickey plays outside". First, by the Law of Syllogism on the first two - statements, we get "If Mickey plays outside, then he needs a bath". Then, by the Law of Detachment with "Mickey plays outside", we can conclude that Mickey needs a bath.

Step1: Apply Law of Detachment

Given "If two angles form a right - angle, then they have a sum of 90" and "∠X and ∠Y form a right - angle", by the Law of Detachment, we can conclude that ∠X+∠Y = 90.

Step2: Apply Law of Syllogism and Detachment

We have "If two angles form a right - angle, then they have a sum of 90", "If two angles have a sum of 90, then they are complementary" and "∠X and ∠Y form a right - angle". First, by the Law of Syllogism on the first two statements, we get "If two angles form a right - angle, then they are complementary". Then, by the Law of Detachment with "∠X and ∠Y form a right - angle", we can conclude that ∠X and ∠Y are complementary.

Step1: Determine lunch choices

We know Clara will not eat sandwiches and Mark won't eat salad or bread. Since there are three lunch options (soup, salad, sandwiches) and each person has a different lunch, Mark must eat soup. Since Clara doesn't eat sandwiches, Clara eats salad and Harold eats sandwiches.

Step2: Determine drink - food pairings

We know the person who had the soup also had the iced tea (Mark had soup, so Mark had iced tea), and the person who had the sandwich also had the milk (Harold had the sandwich, so Harold had the milk). Since each person had a different drink and there are three drinks, the person who had salad (Clara) had mineral water.

Answer:

Conclusion 1: Mickey will get muddy.
Conclusion 2: Mickey needs a bath.

15.