If $a, b$ and $c \in N$ which one of the following is not true ?
- $a \mid b$ and $a|c \Rightarrow a| b+c$
- $a|b+c \Rightarrow a| b$ and $a \mid c$
- $a \mid b$ and $b|c \Rightarrow a| c$
- $a \mid b$ and $a|c \Rightarrow a| 3 b+2 c$
The Correct Option is B
Solution and Explanation
$a | b( + c) \nRightarrow a|b $ and $a|c$
e.g., $6 \, 18 \; \nRightarrow 6| 1$ and $6|17$
Top Questions on Sets
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- Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
- The distance of the point \( (2, 3) \) from the line \( 2x - 3y + 28 = 0 \), measured parallel to the line \( \sqrt{3}x - y + 1 = 0 \), is equal to
- Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The shaded region in the Venn diagram represents
Questions Asked in KCET exam
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- If \(N_2\) gas is bubbled through water at 293 K, how many moles of \(N_2\) gas would dissolve in 1 litre of water? Assume that \(N_2\) exerts a partial pressure of 0.987 bar. [Given \(K_H\) for \(N_2\) at 293 K is 76.48 K bar]
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".