Let S(x, y) denote the statement "x has seen y" and D denote the set of all students in our class and M be the set of all movies. a. Express the following English sentence as a quantified proposition using the definitions above:
"For every movie there is a pair of students in our class who have both seen it." Hint: Use three quantifiers - one for the movie and two for a pair of students.

b. Negate the quantified proposition you wrote for part (a) (i. e., place a "¬" in front of it). Use de Morganâs law for quantifiers to move the negation inside the quantifiers.
c. Translate you answer for part (b) back to plain English.

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

The perimeter of a rectangle is greater than or equal to 74 meters. if the length is 25 meters, the minimum width of the rectangle is meters.

The? half-life of a radioactive substance is 20 years. if you start with some amount of this? substance, what fraction will remain in 120 ? years