Explanation
Solution
Humein set R ke elements ki sankhya batani hai jahan conditions hain: a1≤b2 aur b1≤a2.
Step 1: Problem ko break karna
Relation R ke elements ((a1,b1),(a2,b2)) ke form mein hain. Iska matlab humein do cheezein independentally count karni hain aur phir unhe multiply karna hai:
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a1≤b2 ki kitni pairs ban sakti hain.
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b1≤a2 ki kitni pairs ban sakti hain.
Step 2: a1≤b2 ke liye pairs count karna
a1∈A aur b2∈B hain.
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Agar a1=1, toh b2∈{2,4,5,8,10} (5 values)
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Agar a1=3, toh b2∈{4,5,8,10} (4 values)
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Agar a1=4, toh b2∈{4,5,8,10} (4 values)
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Agar a1=6, toh b2∈{8,10} (2 values)
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Agar a1=9, toh b2∈{10} (1 value)
Total pairs (a1,b2) s.t. a1≤b2:
Step 3: b1≤a2 ke liye pairs count karna
b1∈B aur a2∈A hain.
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Agar b1=2, toh a2∈{3,4,6,9} (4 values)
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Agar b1=4, toh a2∈{4,6,9} (3 values)
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Agar b1=5, toh a2∈{6,9} (2 values)
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Agar b1=8, toh a2∈{9} (1 value)
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Agar b1=10, toh a2∈∅ (0 values)
Total pairs (b1,a2) s.t. b1≤a2:
Step 4: Total elements in R
Kyonki dono conditions "AND" se judi hain aur variables independent hain, total elements honge:
Number of elements=N1×N2
Sahi Option: (2) 160
