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Symbol Notation - Intermediate Level: comparative symbols INTERMEDIATE

Boost your speed and accuracy with this adaptive style 📈 worksheet. Worksheet 15 of 30 presents 20 intermediate-level symbol notation problems. Focus on comparative symbols while practicing symbolic logic, notation puzzles, symbol interpretation. Difficulty: moderate complexity with mixed patterns. Perfect for mid-level test takers.

📝 Worksheet 15 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 15 of 30 (50% complete)

Question 1

Given: A = {1, 2, 4, 5, 7} B = {2, 3, 4, 5} C = {1, 2, 3, 7, 8, 9} Find: A − C
Difference of A and C:
{1, 2, 4, 5, 7} − {1, 2, 3, 7, 8, 9} = {4, 5}
sets, operations

Question 2

If g(x) = x + 5, then find g(4)
Substituting x = 4:
4 + 5 = 9
functions, substitution

Question 3

Given: A = {2, 3, 4, 6, 7, 9} B = {1, 3, 5, 6, 8, 9} C = {1, 3, 6, 7, 8, 10} Find: B ∩ A
Intersection of B and A:
{1, 3, 5, 6, 8, 9} ∩ {2, 3, 4, 6, 7, 9} = {3, 6, 9}
sets, operations

Question 4

If k(x) = x/4, then find k(9)
Substituting x = 9:
9/4 = 2.25
functions, substitution

Question 5

If '≼' means '≤', then determine: 9 ≼ 17
≼ = ≤
9 ≤ 17 is True
inequality, comparison

Question 6

If k(x) = x/4, then find k(6)
Substituting x = 6:
6/4 = 1.50
functions, substitution

Question 7

If '≺' means '<', then determine: 10 ≺ 10
≺ = <
10 < 10 is False
inequality, comparison

Question 8

Given: A = {2, 6, 8} B = {4, 8, 9, 10} C = {1, 2, 4, 5, 6, 7} Find: A ∩ C
Intersection of A and C:
{2, 6, 8} ∩ {1, 2, 4, 5, 6, 7} = {2, 6}
sets, operations

Question 9

If k(x) = x + 2x, then find k(6)
Substituting x = 6:
6 + 26 = 32
functions, substitution

Question 10

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: h(p(g(6)))
Evaluate from innermost outward:
h(p(g(6)))
= 529
nested, functions, advanced

Question 11

If f(x) = x², then find f(4)
Substituting x = 4:
4² = 16
functions, substitution

Question 12

If P = True, Q = True, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=True, Q=True → IFF is True when both are same
Result: True
logic, boolean

Question 13

If ∇ = -, ⊕ = + (standard order of operations applies), then evaluate: 4 ∇ 6 ⊕ 3
Substituting symbols: 4 - 6 + 3
Applying order of operations: = 1
arithmetic, basic

Question 14

If P = False and '!' means NOT, then evaluate: !P
Logical operation: NOT
P=False → NOT flips the value
Result: True
logic, boolean

Question 15

Given matrices: A = [ 2 3] [ 5 4] B = [ 3 3] [ 2 2] Compute: A + B
Matrix addition:
A + B =

[ 5 6]
[ 7 6]
matrix, advanced

Question 16

In the notation system where ♥ means 3x, what is the value of ♥(3)?
Applying ♥ to 3:
33 = 33
complex, systems

Question 17

Given: A = {4, 5, 8} B = {1, 2, 4, 7} C = {4, 5, 6, 9} Find: C △ B
Symmetric Difference of C and B:
{4, 5, 6, 9} △ {1, 2, 4, 7} = {1, 2, 5, 6, 7, 9}
sets, operations

Question 18

Given matrices: A = [ 5 4] [ 1 5] B = [ 3 3] [ 1 1] Compute: A - B
Matrix subtraction:
A - B =

[ 2 1]
[ 0 4]
matrix, advanced

Question 19

Given: A = {5, 6, 7, 8} B = {1, 3, 7, 8, 9} C = {1, 5, 6, 7, 10} Find: C ∪ B
Union of C and B:
{1, 5, 6, 7, 10} ∪ {1, 3, 7, 8, 9} = {1, 3, 5, 6, 7, 8, 9, 10}
sets, operations

Question 20

If P = False, Q = False, and 'nand' means NAND, then evaluate: P nand Q
Logical operation: NAND
P=False, Q=False → NAND is True except when both are True
Result: True
logic, boolean
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