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Symbol Notation - Intermediate-Advanced Level: symbolic representation INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for symbol notation: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: symbolic representation. Develop expertise in notation systems, symbol relationships, logical symbols with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 19 of 30 (63% complete)

Question 1

If '≼' means '≤', then determine: 6 ≼ 3
≼ = ≤
6 ≤ 3 is False
inequality, comparison

Question 2

Given: A = {1, 2, 3, 7, 10} B = {2, 4, 7} C = {1, 4, 8} Find: A − C
Difference of A and C:
{1, 2, 3, 7, 10} − {1, 4, 8} = {2, 3, 7, 10}
sets, operations

Question 3

Given matrices: A = [ 2 3] [ 1 3] B = [ 1 1] [ 5 3] Compute: A + B
Matrix addition:
A + B =

[ 3 4]
[ 6 6]
matrix, advanced

Question 4

If '≻' means '>', then determine: 19 ≻ 2
≻ = >
19 > 2 is True
inequality, comparison

Question 5

In the notation system where ♣ means x/2, what is the value of ♣(3)?
Applying ♣ to 3:
3/2 = 1.50
complex, systems

Question 6

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 7

If g(x) = x/3, then find g(4)
Substituting x = 4:
4/3 = 1.33
functions, substitution

Question 8

If ★ = +, ♢ = + (standard order of operations applies), then evaluate: 1 ★ 1 ♢ 4
Substituting symbols: 1 + 1 + 4
Applying order of operations: = 6
arithmetic, basic

Question 9

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

Question 10

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

Question 11

If '≠' means '≠', then determine: 15 ≠ 5
≠ = ≠
15 ≠ 5 is True
inequality, comparison

Question 12

Given: A = {5, 7, 8} B = {1, 2, 4, 8, 10} C = {2, 4, 10} Find: A △ C
Symmetric Difference of A and C:
{5, 7, 8} △ {2, 4, 10} = {2, 4, 5, 7, 8, 10}
sets, operations

Question 13

In the notation system where ☆ means x², what is the value of ☆(5)?
Applying ☆ to 5:
5² = 25
complex, systems

Question 14

If g(x) = x + 5, then find g(1)
Substituting x = 1:
1 + 5 = 6
functions, substitution

Question 15

If ∇ = -, ◆ = × (standard order of operations applies), then evaluate: 13 ∇ 14 ◆ 15
Substituting symbols: 13 - 14 × 15
Applying order of operations: = -197
arithmetic, basic

Question 16

If h(x) = 2x², then find h(2)
Substituting x = 2:
22² = 484
functions, substitution

Question 17

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

Question 18

Given matrices: A = [ 1 1] [ 2 3] B = [ 4 4] [ 4 1] Compute: A × B
Matrix multiplication:
A × B =

[ 8 5]
[20 11]
matrix, advanced

Question 19

If '≠' means '≠', then determine: 10 ≠ 14
≠ = ≠
10 ≠ 14 is True
inequality, comparison

Question 20

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: g(r(3))
Evaluate from innermost outward:
g(r(3))
= 232
nested, functions, advanced
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