#$&* course mth 151 005. `Query 5
.............................................
Given Solution: `a** There are 10 numbers in the set: 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qQuery 2.5.18 n({x | x is an even integer } YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This set would be infinite. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a** {x | x is an even integer } indicates the set of ALL possible values of the variable x which are even integers. Anything that satisfies the description is in the set. This is therefore the set of even integers, which is infinite. Since this set can be put into 1-1 correspondence with the counting numbers its cardinality is aleph-null. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qQuery 2.5.24 how many diff corresp between {Foxx, Myers, Madonna} and {Powers, Charles, Peron}? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I get 9 pairs. (F,Po), (F, C), (F, Pe), (My, Po), (My, C), (My, Pe), (Ma, Po), (Ma, C), (Ma, Pe) confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a** Listing them in order, according to the order of listing in the set. We have: [ {Foxx, Powers},{Myers, Charles},{Madonna, Perron}] , [{Foxx, Powers},{Myers,Peron},{Madonna, Charles}], [{Foxx, Charles},{Myers, Powers},{Madonna, Peron}] [ {Foxx, Charles},{Myers,Peron},{Madonna,Powers}], [{Foxx, Peron},{Myers, Powers},{Madonna,Charles}], [{Foxx, Peron},{Myers, Charles},{Madonna, Powers}] for a total of six. Reasoning it out, there are three choices for the character paired with Foxx, which leaves two for the character to pair with Myers, leaving only one choice for the character to pair with Madonna. ** STUDENT QUESTION I dont understand what happened to the other 3 choices for pairing. I got (Foxx, Powers) (Foxx, Charles) (Foxx, Peron) (Myers, Powers) (Myers, Charles) (Myers, Peron) (Madonna, Powers) (Madonna, Charles) (Madonna, Peron) INSTRUCTOR RESPONSE What you listed were ordered pairs, one from the first set and one from the second. In fact you listed the 9 pairs of the 'product set'' A X B, an idea you will encounter later in this chapter. However an ordered pair of elements, one from the first set and one from the second (for example your listing (Madonna, Peron)), is not a one-to-one correspondence. In a 1-1 correspondence every element in the first set must be paired with an element in the second. [ {Foxx, Powers},{Myers, Charles},{Madonna, Perron}] is a one-to-one correspondence between the sets. It tells you who each member of the first set is paired with in the second. [{Foxx, Powers},{Myers,Peron},{Madonna, Charles}] is a different one-to-one correspondence. [{Foxx, Charles},{Myers, Powers},{Madonna, Peron}] is another. [ {Foxx, Charles},{Myers,Peron},{Madonna,Powers}], [{Foxx, Peron},{Myers, Powers},{Madonna,Charles}], and [{Foxx, Peron},{Myers, Charles},{Madonna, Powers}] are three more one-to-one correspondences. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I read your notes on the answer but I still don't understand why the answer is 6??????? ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...} YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 ↔ -17 2 ↔ -22 3 ↔ -27..... confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a**You have to describe the 1-1 correspondence, including the rule for the nth number. A complete description might be 1 <-> -17, 2 <-> -22, 3 <-> -27, ..., n <-> -12 + 5 * n. You have to give a rule for the description. n <-> -12 - 5 * n is the rule. Note that we jump by -5 each time, hence the -5n. To get -17 when n=1, we need to start with -12. THE REASONING PROCESS TO GET THE FORMULA: The numbers in the first set decrease by 5 each time so you need -5n. The n=1 number must be -17. -5 * 1 = -5. You need to subtract 12 from -5 to get -17. So the formula is -5 n - 12. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I'm not 100% sure how to do the n thing.... ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...} YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 ↔ -17 2 ↔ -22 3 ↔ -27..... confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a**You have to describe the 1-1 correspondence, including the rule for the nth number. A complete description might be 1 <-> -17, 2 <-> -22, 3 <-> -27, ..., n <-> -12 + 5 * n. You have to give a rule for the description. n <-> -12 - 5 * n is the rule. Note that we jump by -5 each time, hence the -5n. To get -17 when n=1, we need to start with -12. THE REASONING PROCESS TO GET THE FORMULA: The numbers in the first set decrease by 5 each time so you need -5n. The n=1 number must be -17. -5 * 1 = -5. You need to subtract 12 from -5 to get -17. So the formula is -5 n - 12. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I'm not 100% sure how to do the n thing.... ------------------------------------------------ Self-critique Rating: #*&! ********************************************* Question: `q2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...} YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 ↔ -17 2 ↔ -22 3 ↔ -27..... confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a**You have to describe the 1-1 correspondence, including the rule for the nth number. A complete description might be 1 <-> -17, 2 <-> -22, 3 <-> -27, ..., n <-> -12 + 5 * n. You have to give a rule for the description. n <-> -12 - 5 * n is the rule. Note that we jump by -5 each time, hence the -5n. To get -17 when n=1, we need to start with -12. THE REASONING PROCESS TO GET THE FORMULA: The numbers in the first set decrease by 5 each time so you need -5n. The n=1 number must be -17. -5 * 1 = -5. You need to subtract 12 from -5 to get -17. So the formula is -5 n - 12. **