Inequality practice problems( Part I )

Example 1

Statements: N ∂ B, B $ W, W # H, H © M

Conclusions: (1) M @ W.  (2)  H @ N.  (3) W ∂ N.

Step 1 – Make a single statement. 

N ∂ B $ W # H © M

Step 2 – Analyze the conclusions one by one. Always compare with the Modified Statement. 

1. M @ W

• If you draw a line from M to W, you will get a Reverse Line.
• Between M and W two symbols are there. One is © and other is #.  Both are in row 2. Highest Priority is #. Since the letters form a reverse line, we should note the symbol which is exactly above #. The symbol above to # is @. So M @ W is TRUE. 

2. H @ N

• If you draw a line from H to N, you will get a Reverse line.
• Between H and N, the symbols are #, $, and ∂.
• If you check these symbols with the table, # is in Row 2 and $ is in Row 1. So Conclusion 2 is FALSE. 

3. W @ N

• If you draw a line from W to N, you will get a Reverse line.
• Between W and N, the symbols are $ and ∂. Between $ and ∂, the higher priority goes to $.
• The conclusion formed a reverse line. So we should note the symbol which is opposite to $. That is ©. But given conclusion is W @ N. So it is FALSE

So Conclusion one alone Follows

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Example 2

Statements – R © D, D $ J, J # M, M @ K

Conclusions – 1. K # J.   2. D @ M   3. R # M.   4. D @ K

Step 1 – Modify the statement.

R © D $ J # M @ K

Table

Step – 2 – Analyze the conclusion one by one.

1. K # J

• Between K and J – Reverse Line. Symbols are – @ and #.
• In table @ and # are in different rows.
• Conclusion 1 – FALSE

2. D @ M

• Between D and M – Forward Line. Symbols are $ and #.
• In table $ and # are in different rows.
• Conclusion 2 – False.

3. R # M

• Forward line. Symbols are ©, $, and #.
• $ and # are in different rows.
• Conclusion 3 – False.

4. D @ K

• Forward Line. Symbols are $, # and @.
• Symbols are in different rows.
• Conclusion 4 – False.

NOTE: When more than one conclusion in false, check for merging concept. If the characters are same and both the statements are false, and while merging, if we get a meaningful symbol, then the statements can be merged. (To learn clearly about merging, check Syllogism Made Easy). 

In the above problem, all the characters of the statements are different. So we can not merge it. So None is True.