Conditional Rules

Conditional rules represent a step up in complexity from standard compound rules. Rather than two independent conditions that both must hold, a conditional rule takes the form: "IF [condition A], THEN [condition B]." The second condition only applies when the first condition is met. These rules are among the hardest to spot in UCAT AR because they create an inconsistency that looks like randomness unless you recognise the "if-then" structure.

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The Structure of a Conditional Rule

A standard compound rule says: "X is always true AND Y is always true."

A conditional rule says: "IF X is true, THEN Y is also true. If X is not true, Y may or may not be true."

Rule type	Example	How it works
Compound	"All shapes are black AND there are exactly 3 shapes"	Both conditions always hold
Conditional	"IF a circle is present, THEN it is always black"	The circle-is-black rule only applies when a circle exists. Boxes without circles can have any shading.

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Why Conditional Rules Are Hard to Spot

Consider this Set A:

• Box 1: Black circle, white triangle, white square
• Box 2: White pentagon, white hexagon, white rectangle (no circle)
• Box 3: Black circle, white diamond, white arrow
• Box 4: White triangle, white square, white pentagon (no circle)
• Box 5: Black circle, white hexagon
• Box 6: White square, white rectangle, white arrow (no circle)

If you check the colour pattern, it looks inconsistent: some boxes have a mix of black and white, while others are entirely white. There seems to be no clean colour rule.

But look closer: every box that contains a circle has a black circle. Boxes without circles have all-white shapes. The rule is: "IF a circle is present, THEN it is black."

The inconsistency disappears when you recognise the conditional structure.

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Common Conditional Rule Formats

Format 1: Shape Type Determines Shading

"IF [shape type], THEN [specific shading]"

Example	Meaning
"If a triangle, then black"	All triangles are black; other shapes can be any colour
"If curved, then white"	Circles and semi-circles are white; straight shapes can be any colour
"If hexagon, then grey"	Hexagons are grey; other shapes vary

Format 2: Shading Determines Size

"IF [shading], THEN [specific size]"

Example	Meaning
"If black, then large"	Black shapes are always large; white shapes can be any size
"If white, then small"	White shapes are always small; black shapes can be any size

Format 3: Size Determines Position

"IF [size], THEN [specific position]"

Example	Meaning
"If large, then in the centre"	Large shapes always occupy the centre; small shapes can be anywhere
"If small, then in a corner"	Small shapes are always in corners; other shapes are positioned freely

Format 4: Number Determines Another Feature

"IF [count condition], THEN [feature]"

Example	Meaning
"If 3+ shapes, then all are the same colour"	Boxes with 3 or more shapes have uniform shading; boxes with 1-2 shapes may have mixed shading
"If an even number of shapes, then there is at least one circle"	Even-count boxes always include a circle; odd-count boxes may or may not

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Worked Example: "If Triangle, Then Black"

Set A:

• Box 1: Black triangle, white circle, white square (triangle is black ✓)
• Box 2: White pentagon, white hexagon (no triangle — rule does not apply, any colours fine ✓)
• Box 3: Black triangle, black triangle, white diamond (triangles are black ✓)
• Box 4: White circle, white rectangle, white arrow (no triangle ✓)
• Box 5: Black triangle, grey hexagon, white circle (triangle is black ✓)
• Box 6: White pentagon, grey square (no triangle ✓)

Set B:

• Box 1: White triangle, white circle (triangle is white — violates the conditional ✗)
• Box 2: Grey triangle, black square (triangle is grey — violates ✗)
• Box 3: White pentagon, black hexagon (no triangle — but Set B might have its own rule)
• Box 4: White triangle, white diamond, black arrow (triangle is white ✗)
• Box 5: Black circle, grey triangle (triangle is grey ✗)
• Box 6: White rectangle, black triangle (triangle is black — satisfies the condition! But this is Set B)

Wait — Box 6 of Set B has a black triangle. Does that violate Set B's pattern? If Set B's rule is "triangles are NOT black", then Box 6 contradicts it. Let me reconsider.