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(a) (AT)T=A
(b) (A+B)T=AT+BT
(c) (AB)T=BT AT.
Let us denote Sn = an + bn + cn for arbitrary numbers a, b, c.
It is known that S1 = 8, S2 = 66, S3 = 536 for some values of
a, b, c. What is the smallest possible value of S242 — S41 S43?
Let p: I will study
Let q: I will pass the test
Let r: I am foolish
1. I will study or i am foolish
2. I will study or i will not pass the test.
3. I will study and I will pass the test
4. I will past the test or I am foolish
5. I am not foolish and I will pass the test.
6. I will not study or I am foolish
7. I will study or I will not study
8. I will study and I will pass the test or I am foolish.
9. It is not true that i will not study or I am foolish
10. It is not the case that I will not study or I am not foolish
There is an island with two mythical creatures, the Komos and the Dragos. Komos loves eating visitors to the island while Dragos hates to eat visitors. One fine day, you mysteriously end up on the island and encounter two creatures, Blue and Red. The Blue creature smiles and tell you, “Don’t be afraid! We both are not human eaters”. Determine, if possible, whether the Blue and Red creatures is a Komos or a Dragos.
Let p: I will study.
Let q: I will pass the test.
Let r: I am foolish.
1. I will study or I am foolish.
2. I will study or I will not pass the test.
3. I will study and I will pass the test.
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MATHEMATICS IN THE MODERN WORLD
4. I will past the test or I am foolish.
5. I am not foolish and I will pass the test.
6. I will not study or I am foolish.
7. I will study or I will not study.
8. I will study and I will pass the test, or I am foolish.
9. 9. It is not true that I will study or I am foolish.
10. It is not the case that I will not study or I am not foolish.
Let p: I will study.
Let q: I will pass the test.
Let r: I am foolish.
1. I will study or I am foolish.
2. I will study or I will not pass the test.
3. I will study and I will pass the test.
Page 1
MATHEMATICS IN THE MODERN WORLD
4. I will past the test or I am foolish.
5. I am not foolish and I will pass the test.
6. I will not study or I am foolish.
7. I will study or I will not study.
8. I will study and I will pass the test, or I am foolish.
9. 9. It is not true that I will study or I am foolish.
10. It is not the case that I will not study or I am not foolish.
in a class of 35 students, each student studies Chemistry or woodwork. Twice as many study chemistry as study woodwork and half as many study only chemistry as study both. illustrate the information on a venn diagram and hence find the number of students who study both subjects.
