The mechanics are really simple. Based on the given statement, tell me which is the appropriate Venn Diagram. The 3 best explanations will win a limited edition 2011 UP Back2Back2Black Cheerdance Competition Shirt. No kidding.
So here’s the statement: CONFIDENCE IS A COMPONENT OF ARROGANCE.
Diagram A
Diagram B
Also, to make things fair, comments / answers will be approved and revealed all at the same time. Meaning, all replies are concealed until we judge who the winners are.
And again, these are Venn Diagrams.
AND THE ANSWER:
No one got it. Sorry.
Advertisement
Diagram B.
“Confidence is a component of arrogance.”
As defined by the Merriam-Webster Dictionary [http://www.merriam-webster.com/dictionary/component], the word ‘component’ translates to ‘a constituent part’. From the same source, “constituent” means “an essential part”. And “essential” means “of the utmost importance: basic, indispensable, necessary”. Therefore, plugging the words into the statement, we have, “Confidence is a basic, indispensable, necessary part of arrogance”.
Now we define the word subset. According to Wolfram Mathworld [http://mathworld.wolfram.com/Subset.html], the word ‘subset’ pertains to a “portion of a set”, wherein “B (an arbitrary set) is a subset of A (another arbitrary set) *if an only if* every member (or element) of B is a member (or element) of A”. Then, assuming Diagram B, we assume Confidence and Arrogance to be two sets, and let B = Confidence set and A = Arrogance set.
Also, the words, “part” and “component” are synonymous to the word, “element” (according to the Merriam-Webster dictionary). Further, “part” is defined by the same dictionary as “essential portion”. And “element” is defined by Wolfram Mathworld [http://mathworld.wolfram.com/Element.html] as “if x is a member of set A (meaning it is contained by set A), then x is said to be an element of set A”.
Transforming the original statement, we have “Confidence Set is a basic, indispensable, necessary part of Arrogance Set.” We assume the elements of B (confidence set). Since all the elements of the B are in B, then we can transform the statement into, “(All the elements of B) are a basic, indispensable, necessary part of (A)”. And, given the above definitions and synonyms, we can further transform it into, “All the elements of B are basic, indispensable, necessary elements of A”.
In simpler Mathematical terms, “All the elements of B are basic, indispensable, necessary elements of A” can be transformed into, “Every member of B is a member of A”.
In Math 109, “if and only if” is a biconditional logical connective between two statements, wherein the truth of one statement requires the truth of the other, and vice versa. Thus, the definition of subset can be transformed into ” (1st statement) B can only be a subset of A if (2nd statement) every element of B is an element of A. If not every element of B is an element of A, then B is not a subset of A.” Therefore, given these, since the second statement, “Every member of B is a member of A” has been proven to be true, then the first statement, “B is a subset of A”, must also be true. Therefore, transforming the statements in order:
“B is a subset of A since every member of B is a member of A”
“Confidence set is a subset of Arrogance set since all the elements of B are basic, indispensable, necessary elements of A.”
“Confidence is a subset of Arrogance since Confidence Set is a basic, indispensable, necessary part of Arrogance Set.”
“Confidence is a subset of Arrogance since Confidence is an essential part of Arrogance.”
“Confidence is a subset of Arrogance since Confidence is a component of Arrogance.”
Therefore, confidence is a subset of arrogance and Diagram B is the appropriate Venn Diagram.
The only problem is whether Confidence is supposed to be a proper or improper subset. Regardless of that, it is sure, logically, that Diagram A cannot happen according to the given statement.
Thanks xiaobaihua for your submitting your answer.
When one said that “CONFIDENCE IS A COMPONENT OF ARROGANCE”, his statement implies that the former is one of the factors that create, describe, or define the latter. Statistically, when we assume that ARROGANCE is a set, we can say that Set ARROGANCE is a well-defined collection of characteristics, among them is the element CONFIDENCE. To put it in statistical-ese or mathematical-ese terms we have:
ARROGANCE (Y) = { A, B, CONFIDENCE, D, E…} where letters are attributes (or component) of ARROGANCE
Assuming, not implying, that there are no factors that should be considered in the given set and there are no assigned values to personal traits, we could draw Set ARROGANCE as DIAGRAM B.
PS. Besides in real life, arrogance is characterized by aspects beyond the ambit of confidence. To be confident is essentially to be comfortable with oneself — through competence, experience or knowledge. Arrogance, however, requires more than just comfort as provided by self-awareness; arrogance requires (at least) the NEED to be right, the YEARNING to be heard and the DESIRE to win over others [through any means necessary] in addition to being confident. Of course, the entire notion and attributable elements to “arrogance” is subject to a plethora of debates, but given the premise and statement provided above, the explanation would suffice.
Thanks MDGamboa for your submitting your answer.
Is this still ongoing? I’m not in the PH right now.
Hello, for those inquiring, yes this is still open. Still waiting for other answers. Maybe Ill announce the winner Sunday night.
For those who are outside the Philippines, I can ship the shirt to you. Just handle the shipping costs. (Dont worry, I’m legit lol)
hi, can you remove my post? i didnt know it would be public and since the contest is over anyway, no need for my name to be out there! thanks!
not sure i’m doing this right, but i’m voting B.
stating something is a component of something else is the same as saying it’s a part of that thing….not saying it encompasses it, like diagram A.